http://www.cds.caltech.edu/~murray/wiki/api.php?action=feedcontributions&user=Sinopoli&feedformat=atomMurrayWiki - User contributions [en]2020-03-29T22:28:25ZUser contributionsMediaWiki 1.23.12http://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_Control:_the_UDP_caseNCS: Packet-based Control: the UDP case2006-05-07T00:50:22Z<p>Sinopoli: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture we consider the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We focus on the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon the results shown in the previous lecture on estimation with unreliable communication, we show the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.<br />
In the previous lectures we showed that, for protocols where<br />
packets are acknowledged at the receiver (e.g.\ TCP type<br />
protocols), the separation principle holds. Moreover, the optimal<br />
LQG control is a linear function of the state. Finally, we showed the existence of critical arrival<br />
probabilities below which the optimal controller fails to<br />
stabilize the system. In this lecture we focus on UDP-like protocols. It turns out that when there is no feedback on whether a control packet has been delivered or not<br />
(e.g. UDP type protocols), the LQG optimal controller is in<br />
general nonlinear function of the information state. In the particular case where there is no measurement noise and the observation matrix C is invertible, we are able to show that the optimal controller is again linear, even if the separation principle still doesn't hold.<br />
Necessary conditions on the arrival probabilities for state boundedness are provided.<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-3_packet_based_control_slides.pdf |Lecture: UDP Packet-based Control slides]]<br />
* [[Media:L5-2_packet_based_control.pdf |Lecture: TCP/UDP Packet-based Control]]<br />
For this lecture consider pages 71-88.<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/Sinopoli_ifac.pdf LQG Control with Missing Observation and Control Packets], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. Ifac 05</p><br />
<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/cdc05.pdf An LQG Optimal Linear Controller for Control Systems with Packet Losses], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. CDC 05</p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<br />
* [[Media:Nilsson_thesis_98.pdf | Real-Time Control Systems with Delays]], by Johan Nilsson, PhD Thesis.<br />
<br />
==Books==<br />
* <p> Stochastic Systems: Estimation, Identification and Adaptive Control, by P.R. Kumar, P. Varaiya, Prentice Hall, 1986. Difficult to find (Richard has a copy though). Even if it is not the most user friendly reading, chapters 6 to 8 contain a good reference for dynamic programming and LQG control.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529086/qid=1146074615/sr=2-2/ref=pd_bbs_b_2_2/103-1985563-9207029?s=books&v=glance&n=283155 Dynamic Programming and Optimal Control], by D. Bertsekas. </p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529108/qid=1146074615/sr=1-9/ref=sr_1_9/103-1985563-9207029?s=books&v=glance&n=283155 Neuro-Dynamic Programming], by D. Bertsekas and J. Tsitsiklis. </p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=File:L5-3_packet_based_control_slides.pdfFile:L5-3 packet based control slides.pdf2006-05-07T00:48:59Z<p>Sinopoli: </p>
<hr />
<div></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_Control:_the_UDP_caseNCS: Packet-based Control: the UDP case2006-05-07T00:47:35Z<p>Sinopoli: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture we consider the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We focus on the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon the results shown in the previous lecture on estimation with unreliable communication, we show the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.<br />
In the previous lectures we showed that, for protocols where<br />
packets are acknowledged at the receiver (e.g.\ TCP type<br />
protocols), the separation principle holds. Moreover, the optimal<br />
LQG control is a linear function of the state. Finally, we showed the existence of critical arrival<br />
probabilities below which the optimal controller fails to<br />
stabilize the system. In this lecture we focus on UDP-like protocols. It turns out that when there is no feedback on whether a control packet has been delivered or not<br />
(e.g. UDP type protocols), the LQG optimal controller is in<br />
general nonlinear function of the information state. In the particular case where there is no measurement noise and the observation matrix C is invertible, we are able to show that the optimal controller is again linear, even if the separation principle still doesn't hold.<br />
Necessary conditions on the arrival probabilities for state boundedness are provided.<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-3_packet_based_control_slides.pdf |Lecture: UDP Packet-based Control slides]]<br />
* [[Media:L5-2_packet_based_control.pdf |Lecture: TCP/UDP Packet-based Control]],<br />
For this lecture consider pages 71-88.<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/Sinopoli_ifac.pdf LQG Control with Missing Observation and Control Packets], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. Ifac 05</p><br />
<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/cdc05.pdf An LQG Optimal Linear Controller for Control Systems with Packet Losses], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. CDC 05</p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<br />
* [[Media:Nilsson_thesis_98.pdf | Real-Time Control Systems with Delays]], by Johan Nilsson, PhD Thesis.<br />
<br />
==Books==<br />
* <p> Stochastic Systems: Estimation, Identification and Adaptive Control, by P.R. Kumar, P. Varaiya, Prentice Hall, 1986. Difficult to find (Richard has a copy though). Even if it is not the most user friendly reading, chapters 6 to 8 contain a good reference for dynamic programming and LQG control.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529086/qid=1146074615/sr=2-2/ref=pd_bbs_b_2_2/103-1985563-9207029?s=books&v=glance&n=283155 Dynamic Programming and Optimal Control], by D. Bertsekas. </p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529108/qid=1146074615/sr=1-9/ref=sr_1_9/103-1985563-9207029?s=books&v=glance&n=283155 Neuro-Dynamic Programming], by D. Bertsekas and J. Tsitsiklis. </p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_Control:_the_TCP_caseNCS: Packet-based Control: the TCP case2006-05-07T00:44:52Z<p>Sinopoli: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture we consider the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We focus on the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon the results shown in the previous lecture on estimation with unreliable communication, we show the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-2_packet_based_control_slides.pdf |Lecture: TCP Packet-based Control slides]]<br />
* [[Media:L5-2_packet_based_control.pdf |Lecture: TCP/UDP Packet-based Control notes]],<br />
For this lecture consider pages 57-71.<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/acc05.pdf Optimal Control with Unreliable Communication: the TCP Case], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. This is the paper where we published the results contained in the thesis</p><br />
<br />
<br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<br />
* [[Media:Nilsson_thesis_98.pdf | Real-Time Control Systems with Delays]], by Johan Nilsson, PhD Thesis.<br />
<br />
==Books==<br />
* <p> Stochastic Systems: Estimation, Identification and Adaptive Control, by P.R. Kumar, P. Varaiya, Prentice Hall, 1986. Difficult to find (Richard has a copy though). Even if it is not the most user friendly reading, chapters 6 to 8 contain a good reference for dynamic programming and LQG control.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529086/qid=1146074615/sr=2-2/ref=pd_bbs_b_2_2/103-1985563-9207029?s=books&v=glance&n=283155 Dynamic Programming and Optimal Control], by D. Bertsekas. </p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529108/qid=1146074615/sr=1-9/ref=sr_1_9/103-1985563-9207029?s=books&v=glance&n=283155 Neuro-Dynamic Programming], by D. Bertsekas and J. Tsitsiklis. </p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_Control:_the_TCP_caseNCS: Packet-based Control: the TCP case2006-05-07T00:44:22Z<p>Sinopoli: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture we consider the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We focus on the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon the results shown in the previous lecture on estimation with unreliable communication, we show the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-2_packet_based_control_slides.pdf |Lecture: TCP Packet-based Control slides]]<br />
* [[Media:L5-2_packet_based_control.pdf |Lecture: Packet-based Control notes]],<br />
For this lecture consider pages 57-71.<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/acc05.pdf Optimal Control with Unreliable Communication: the TCP Case], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. This is the paper where we published the results contained in the thesis</p><br />
<br />
<br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<br />
* [[Media:Nilsson_thesis_98.pdf | Real-Time Control Systems with Delays]], by Johan Nilsson, PhD Thesis.<br />
<br />
==Books==<br />
* <p> Stochastic Systems: Estimation, Identification and Adaptive Control, by P.R. Kumar, P. Varaiya, Prentice Hall, 1986. Difficult to find (Richard has a copy though). Even if it is not the most user friendly reading, chapters 6 to 8 contain a good reference for dynamic programming and LQG control.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529086/qid=1146074615/sr=2-2/ref=pd_bbs_b_2_2/103-1985563-9207029?s=books&v=glance&n=283155 Dynamic Programming and Optimal Control], by D. Bertsekas. </p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529108/qid=1146074615/sr=1-9/ref=sr_1_9/103-1985563-9207029?s=books&v=glance&n=283155 Neuro-Dynamic Programming], by D. Bertsekas and J. Tsitsiklis. </p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=File:L5-2_packet_based_control_slides.pdfFile:L5-2 packet based control slides.pdf2006-04-28T08:04:35Z<p>Sinopoli: </p>
<hr />
<div></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_Control:_the_TCP_caseNCS: Packet-based Control: the TCP case2006-04-28T08:03:40Z<p>Sinopoli: /* Lecture Materials */</p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture we consider the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We focus on the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon the results shown in the previous lecture on estimation with unreliable communication, we show the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-2_packet_based_control_slides.pdf |Lecture: Packet-based Control slides]]<br />
* [[Media:L5-2_packet_based_control.pdf |Lecture: Packet-based Control notes]],<br />
For this lecture consider pages 57-71.<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/acc05.pdf Optimal Control with Unreliable Communication: the TCP Case], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. This is the paper where we published the results contained in the thesis</p><br />
<br />
<br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<br />
* [[Media:Nilsson_thesis_98.pdf | Real-Time Control Systems with Delays]], by Johan Nilsson, PhD Thesis.<br />
<br />
==Books==<br />
* <p> Stochastic Systems: Estimation, Identification and Adaptive Control, by P.R. Kumar, P. Varaiya, Prentice Hall, 1986. Difficult to find (Richard has a copy though). Even if it is not the most user friendly reading, chapters 6 to 8 contain a good reference for dynamic programming and LQG control.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529086/qid=1146074615/sr=2-2/ref=pd_bbs_b_2_2/103-1985563-9207029?s=books&v=glance&n=283155 Dynamic Programming and Optimal Control], by D. Bertsekas. </p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529108/qid=1146074615/sr=1-9/ref=sr_1_9/103-1985563-9207029?s=books&v=glance&n=283155 Neuro-Dynamic Programming], by D. Bertsekas and J. Tsitsiklis. </p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_Control:_the_TCP_caseNCS: Packet-based Control: the TCP case2006-04-28T08:03:23Z<p>Sinopoli: /* Lecture Materials */</p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture we consider the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We focus on the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon the results shown in the previous lecture on estimation with unreliable communication, we show the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-2_packet_based_control_slides.pdf |Lecture: Packet-based Control slides]]<br />
<br />
<br />
* [[Media:L5-2_packet_based_control.pdf |Lecture: Packet-based Control notes]],<br />
For this lecture consider pages 57-71.<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/acc05.pdf Optimal Control with Unreliable Communication: the TCP Case], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. This is the paper where we published the results contained in the thesis</p><br />
<br />
<br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<br />
* [[Media:Nilsson_thesis_98.pdf | Real-Time Control Systems with Delays]], by Johan Nilsson, PhD Thesis.<br />
<br />
==Books==<br />
* <p> Stochastic Systems: Estimation, Identification and Adaptive Control, by P.R. Kumar, P. Varaiya, Prentice Hall, 1986. Difficult to find (Richard has a copy though). Even if it is not the most user friendly reading, chapters 6 to 8 contain a good reference for dynamic programming and LQG control.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529086/qid=1146074615/sr=2-2/ref=pd_bbs_b_2_2/103-1985563-9207029?s=books&v=glance&n=283155 Dynamic Programming and Optimal Control], by D. Bertsekas. </p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529108/qid=1146074615/sr=1-9/ref=sr_1_9/103-1985563-9207029?s=books&v=glance&n=283155 Neuro-Dynamic Programming], by D. Bertsekas and J. Tsitsiklis. </p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Template:NCS:_Packet-based_Control:_the_UDP_case_PreviousTemplate:NCS: Packet-based Control: the UDP case Previous2006-04-28T08:00:42Z<p>Sinopoli: </p>
<hr />
<div>NCS: Packet-based Control: the TCP case|Packet-based control TCP</div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Template:NCS:_Packet-based_Control:_the_TCP_case_NextTemplate:NCS: Packet-based Control: the TCP case Next2006-04-28T08:00:08Z<p>Sinopoli: </p>
<hr />
<div>NCS: Packet-based Control: the UDP case|Packet-based control UDP</div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Template:NCS:_Packet-based_Control:_the_TCP_case_PreviousTemplate:NCS: Packet-based Control: the TCP case Previous2006-04-28T07:57:50Z<p>Sinopoli: </p>
<hr />
<div>NCS: Packet-based Estimation|Packet-based Estimation</div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_Control:_the_TCP_caseNCS: Packet-based Control: the TCP case2006-04-28T07:56:29Z<p>Sinopoli: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture we consider the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We focus on the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon the results shown in the previous lecture on estimation with unreliable communication, we show the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-2_packet_based_control.pdf |Lecture: Packet-based Control]],<br />
For this lecture consider pages 57-71.<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/acc05.pdf Optimal Control with Unreliable Communication: the TCP Case], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. This is the paper where we published the results contained in the thesis</p><br />
<br />
<br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<br />
* [[Media:Nilsson_thesis_98.pdf | Real-Time Control Systems with Delays]], by Johan Nilsson, PhD Thesis.<br />
<br />
==Books==<br />
* <p> Stochastic Systems: Estimation, Identification and Adaptive Control, by P.R. Kumar, P. Varaiya, Prentice Hall, 1986. Difficult to find (Richard has a copy though). Even if it is not the most user friendly reading, chapters 6 to 8 contain a good reference for dynamic programming and LQG control.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529086/qid=1146074615/sr=2-2/ref=pd_bbs_b_2_2/103-1985563-9207029?s=books&v=glance&n=283155 Dynamic Programming and Optimal Control], by D. Bertsekas. </p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529108/qid=1146074615/sr=1-9/ref=sr_1_9/103-1985563-9207029?s=books&v=glance&n=283155 Neuro-Dynamic Programming], by D. Bertsekas and J. Tsitsiklis. </p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_Control:_the_UDP_caseNCS: Packet-based Control: the UDP case2006-04-28T07:54:30Z<p>Sinopoli: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture we consider the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We focus on the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon the results shown in the previous lecture on estimation with unreliable communication, we show the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.<br />
In the previous lectures we showed that, for protocols where<br />
packets are acknowledged at the receiver (e.g.\ TCP type<br />
protocols), the separation principle holds. Moreover, the optimal<br />
LQG control is a linear function of the state. Finally, we showed the existence of critical arrival<br />
probabilities below which the optimal controller fails to<br />
stabilize the system. In this lecture we focus on UDP-like protocols. It turns out that when there is no feedback on whether a control packet has been delivered or not<br />
(e.g. UDP type protocols), the LQG optimal controller is in<br />
general nonlinear function of the information state. In the particular case where there is no measurement noise and the observation matrix C is invertible, we are able to show that the optimal controller is again linear, even if the separation principle still doesn't hold.<br />
Necessary conditions on the arrival probabilities for state boundedness are provided.<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-2_packet_based_control.pdf |Lecture: Packet-based Control]],<br />
For this lecture consider pages 71-88.<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/Sinopoli_ifac.pdf LQG Control with Missing Observation and Control Packets], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. Ifac 05</p><br />
<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/cdc05.pdf An LQG Optimal Linear Controller for Control Systems with Packet Losses], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. CDC 05</p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<br />
* [[Media:Nilsson_thesis_98.pdf | Real-Time Control Systems with Delays]], by Johan Nilsson, PhD Thesis.<br />
<br />
==Books==<br />
* <p> Stochastic Systems: Estimation, Identification and Adaptive Control, by P.R. Kumar, P. Varaiya, Prentice Hall, 1986. Difficult to find (Richard has a copy though). Even if it is not the most user friendly reading, chapters 6 to 8 contain a good reference for dynamic programming and LQG control.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529086/qid=1146074615/sr=2-2/ref=pd_bbs_b_2_2/103-1985563-9207029?s=books&v=glance&n=283155 Dynamic Programming and Optimal Control], by D. Bertsekas. </p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529108/qid=1146074615/sr=1-9/ref=sr_1_9/103-1985563-9207029?s=books&v=glance&n=283155 Neuro-Dynamic Programming], by D. Bertsekas and J. Tsitsiklis. </p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_270-2,_Spring_2006CDS 270-2, Spring 20062006-04-28T07:52:51Z<p>Sinopoli: </p>
<hr />
<div><table width="100%" cellspacing=0><br />
<tr valign=top><br />
<td rowspan=2 align=center> [[Image:citlogo.png|75px]]<br />
<td align=center><font color='blue' size='+2'>Networked Control Systems</font><br />
<td rowspan=2 align=center> [[Image:cdslogo.png|90px]]<br />
<tr valign=top><td align=center><font color='blue' size='+1'>Spring 2006</font><br />
</table><br />
<br />
<table align=right><tr><td>__TOC__</table><br />
<table cellspacing=0 cellpadding=0><br />
<tr valign=top><br />
<td width=60%><br />
* Instructor: [[User:Murray|Richard M. Murray]]<br />
* Co-instructors: [[User:Keviczky|Tamas Keviczky]], [[User:Mostofi|Yasi Mostofi]], [[User:Sandberg|Henrik Sandberg]], [[User:Sinopoli|Bruno Sinopoli]]<br />
<td align=center><br />
<table cellpadding=0 cellspacing=0><tr><td><br />
* [[Media:cds270-2_syllabus_sp06.pdf|Course syllabus]]<br />
* [http://listserv.cds.caltech.edu/mailman/listinfo/cds270 Course mailing list]<br />
* [[CDS 270: Information for Lecturers|Information for lecturers]]<br />
</table><br />
<tr><td colspan=2><br />
* Graduate instructors: Vijay Gupta, Zhipu Jin, Ling Shi, Demetri Spanos<br />
* Lectures: MWF 2-3 pm, 125 Steele<br />
</table><br />
<br />
== Course Schedule ==<br />
<br />
{| border=1 width=100%<br />
|-<br />
| Week || Date || Topic || Reading<br />
|-<br />
| align=center rowspan=5 | 1 <br />
| colspan=3 | '''Introduction to Networked Control Systems (R. Murray)'''<br />
|-<br />
| 27 Mar (M)<br />
| [[NCS: Introduction|Course overview, applications and administration]]<br />
| [[Media:cds270-2_syllabus_sp06.pdf|Syllabus]]; {{ncsbook|introduction|Ch 1}}<br />
|-<br />
| 29 Mar (W)<br />
| [[Alice: Introduction|Case study: Alice]]<br />
| [http://www.cds.caltech.edu/~murray/papers/2005t_cre+06-jfr.html Cremean et al, 2005]<br />
|-<br />
| colspan=3 | '''Networked embedded systems programming (R. Murray)'''<br />
|-<br />
| 31 Mar (F)<br />
| [[NCS: Message Transfer Systems|Message transfer systems: spread]]<br />
| {{ncsbook|embedded|Ch 2}}; [http://portal.acm.org/citation.cfm?id=359563 Lamport, 1978]<br />
|-<br />
| align=center rowspan=3 | 2<br />
| 3 Apr (M)<br />
| [[NCS: Multi-Threaded Control Systems|Multi-threaded control systems: pthreads]]<br />
| {{ncsbook|embedded|Ch 2}}; [http://www.llnl.gov/computing/tutorials/pthreads Pthreads]<br />
|-<br />
| 5 Apr (W)<br />
| [[Alice: Vehicle Control|Alice: adrive, astate, trajFollower]]<br />
| {{ncsbook|alice|App A}}; [http://gc.caltech.edu/wiki/index.php/Alice GCwiki]<br />
|-<br />
| 7 Apr* (F)<br />
| No class<br />
| <br />
|-<br />
| align=center rowspan=4 | 3<br />
| colspan=3 | '''Real-time trajectory generation and receding horizon control (R. Murray)'''<br />
|-<br />
| 10 Apr (M)<br />
| [[NCS: Real-Time Trajectory Generation|Real-time trajectory generation]]<br />
| {{ncsbook|trajgen|Ch 3}}<br />
|-<br />
| 12 Apr* (W)<br />
| [[NCS: Receding Horizon Control|Receding horizon control]] (T. Keviczky)<br />
| {{ncsbook|trajgen|Ch 3}}<br />
|-<br />
| 14 Apr (F)<br />
| [[Alice: Path Planning|Alice: plannerModule]]<br />
| {{ncsbook|alice|App A}}; [http://grandchallenge.caltech.edu/wiki/images/b/b3/Thesis.pdf Kogan, 2005]<br />
|-<br />
| align=center rowspan=4 | 4<br />
| colspan=3 | '''State estimation (H. Sandberg)'''<br />
|-<br />
| 17 Apr (M)<br />
| [[NCS: Kalman Filtering|Kalman filtering]]<br />
| {{ncsbook|estim|Ch 4}}; [http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf Welch and Bishop]<br />
|-<br />
| 19 Apr (W)<br />
| [[NCS: Moving Horizon Estimation|Moving horizon estimation]] <br />
| {{ncsbook|estim|Ch 4}}<br />
|-<br />
| 21 Apr (F) <br />
| [[Alice: Road Following|Alice: roadFollowing]] (L. Cremean)<br />
| {{ncsbook|alice|App A}}<br />
|-<br />
| align=center rowspan=4 | 5<br />
| colspan=3 | '''Packet-based estimation and control, I (B. Sinopoli)'''<br />
|-<br />
| 24 Apr (M)<br />
| [[NCS: Packet-based Estimation| Packet-based estimation]]<br />
| {{ncsbook|pack_estim|Ch 5}} <br />
|-<br />
| 26 Apr (W)<br />
| [[NCS: Packet-based Control: the TCP case|Packet-based Control: the TCP case]] <br />
| {{ncsbook|pack_cont|Ch 5}}<br />
|-<br />
| 28 Apr (F) <br />
| [[NCS: Packet-based Control: the UDP case|Packet-based Control: the UDP case]]<br />
| {{ncsbook|pack_cont2|Ch 5}}<br />
|-<br />
| align=center rowspan=4 | 6<br />
| colspan=3 | '''Packet-based estimation and control, II (L. Shi, Y. Mostofi)'''<br />
{{MWFrow|<br />
week=6|<br />
mondate=1 May*|montopic=|monreading=|<br />
weddate=3 May|wedtopic=|wedreading=|<br />
fridate=5 May|fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 7<br />
| colspan=3 | '''Distributed estimation and control (V. Gupta)'''<br />
{{MWFrow|<br />
week=7|<br />
mondate=8 May*|montopic=|monreading=|<br />
weddate=10 May*|wedtopic=|wedreading=|<br />
fridate=12 May |fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 8<br />
| colspan=3 | '''Cooperative control of multi-agent systems (Z. Jin, T. Keviczky)'''<br />
{{MWFrow|<br />
week=8|<br />
mondate=15 May|montopic=|monreading=|<br />
weddate=17 May*|wedtopic=|wedreading=|<br />
fridate=19 May|fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 9<br />
| colspan=3 | '''Project Presentations (All)'''<br />
{{MWFrow|<br />
week=9|<br />
mondate=22 May|montopic=No class|monreading=|<br />
weddate=24 May|wedtopic=Project presentations|wedreading=|<br />
fridate=26 May|fritopic=Project presentations|frireading=|<br />
}}<br />
|}<br />
<br />
== Course Description ==<br />
<br />
Increases in fast and inexpensive computing and communications have enabled a new generation information-rich control systems that rely on multi-threaded networked execution, distributed optimization, adaptation and learning, and contingency management in increasingly sophisticated ways. This course will describe a framework for building such systems and lay out some of the challenges to control theory that must be addressed to enable systematic design and analysis. Two examples will be used to illustrate the results and to serve as testbeds for course projects: [[Alice]], an autonomous vehicle that competed in the 2005 DARPA Grand<br />
Challenge and [[RoboFlag]], a robotic version of capture the flag. Key features of these systems include highly sensory-driven, information rich feedback systems, higher levels of decision making for goal and contingency management, and multi-threaded, networked control architectures.<br />
<br />
== Course Administration ==<br />
<br />
This course is a special topics course in which advanced students will prepare and present much of the lecture material. There is no required homework and no midterm or final exam. Course grades will be based on a course project.<br />
<br />
== Course Project ==<br />
<br />
All students in the course will demonstrate their knowledge of the material by analyzing or implementing a networked control system algorithm. Two testbeds are available for use by the class:<br />
<br />
* <p> '''[[Alice]]''' - Alice is an autonomous vehicle that was built by [http://team.caltech.edu Caltech undergraduates] to compete in the 2005 DARPA Grand Challenge. It is fully equipped with multiple terrain sensing cameras and LADARS, two GPS units and an inertial measurement unit (IMU) for measuring position and orientation, and 10 CPUs of computing horsepower inteconnected by a 1 Gb/s ethernet network. A module software architecture allows new functionality to be implemented and tested with relative ease. Requires knowledge of C/C++ programming under linux.</p><br />
<br />
* <p> '''[[RoboFlag]]''' - RoboFlag is a robotic version of capture the flag in which teams of 6-8 robots with 1-2 humans compete against a like team. A high fidelity simulator is available that allow full simulation of the dynamics, sensing and communications subsystems, providing realistic operation. Features include limited bitrate communication channels, limited sensor range for detecting opposing robots, and a graphical user interface for human-in-the-loop operation. Required knowlege of C/C++ program under Windows.</p><br />
<br />
'''Project ideas''' (will be expanded during the term)<br />
* Benchmark the performance of different messaging protocols (eg, broadcast, UDP, TCP) for communicating the state and terrain data on Alice<br />
* Implement and analyze the effect of "shock absobers" (control buffers, state estimators) on RoboFlag<br />
* Implement state estimation and/or multi-description coding on Alice to handle lost packets of terrain data<br />
<br />
<span id=archive /><br />
<br />
[[Category:Courses]] [[Category:2005-06 Courses]]</div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Template:NCS:_Packet-based_Control:_the_TCP_case_NextTemplate:NCS: Packet-based Control: the TCP case Next2006-04-28T07:51:09Z<p>Sinopoli: </p>
<hr />
<div></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Template:NCS:_Packet-based_Control:_the_TCP_case_PreviousTemplate:NCS: Packet-based Control: the TCP case Previous2006-04-28T07:50:51Z<p>Sinopoli: </p>
<hr />
<div>NCS: Packet-based Control: the TCP case|Packet-based control TCP</div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_Control:_the_TCP_caseNCS: Packet-based Control: the TCP case2006-04-28T07:49:12Z<p>Sinopoli: /* Reading */</p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture we consider the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We focus on the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon the results shown in the previous lecture on estimation with unreliable communication, we show the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.<br />
In the previous lectures we showed that, for protocols where<br />
packets are acknowledged at the receiver (e.g.\ TCP type<br />
protocols), the separation principle holds. Moreover, the optimal<br />
LQG control is a linear function of the state. Finally, we showed the existence of critical arrival<br />
probabilities below which the optimal controller fails to<br />
stabilize the system. In this lecture we focus on UDP-like protocols. It turns out that when there is no feedback on whether a control packet has been delivered or not<br />
(e.g. UDP type protocols), the LQG optimal controller is in<br />
general nonlinear function of the information state. In the particular case where there is no measurement noise and the observation matrix C is invertible, we are able to show that the optimal controller is again linear, even if the separation principle still doesn't hold.<br />
Necessary conditions on the arrival probabilities for state boundedness are provided.<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-2_packet_based_control.pdf |Lecture: Packet-based Control]],<br />
For this lecture consider pages 71-88.<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/Sinopoli_ifac.pdf LQG Control with Missing Observation and Control Packets], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. Ifac 05</p><br />
<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/cdc05.pdf An LQG Optimal Linear Controller for Control Systems with Packet Losses], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. CDC 05</p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<br />
* [[Media:Nilsson_thesis_98.pdf | Real-Time Control Systems with Delays]], by Johan Nilsson, PhD Thesis.<br />
<br />
==Books==<br />
* <p> Stochastic Systems: Estimation, Identification and Adaptive Control, by P.R. Kumar, P. Varaiya, Prentice Hall, 1986. Difficult to find (Richard has a copy though). Even if it is not the most user friendly reading, chapters 6 to 8 contain a good reference for dynamic programming and LQG control.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529086/qid=1146074615/sr=2-2/ref=pd_bbs_b_2_2/103-1985563-9207029?s=books&v=glance&n=283155 Dynamic Programming and Optimal Control], by D. Bertsekas. </p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529108/qid=1146074615/sr=1-9/ref=sr_1_9/103-1985563-9207029?s=books&v=glance&n=283155 Neuro-Dynamic Programming], by D. Bertsekas and J. Tsitsiklis. </p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_Control:_the_TCP_caseNCS: Packet-based Control: the TCP case2006-04-28T07:45:38Z<p>Sinopoli: /* Lecture Materials */</p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture we consider the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We focus on the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon the results shown in the previous lecture on estimation with unreliable communication, we show the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.<br />
In the previous lectures we showed that, for protocols where<br />
packets are acknowledged at the receiver (e.g.\ TCP type<br />
protocols), the separation principle holds. Moreover, the optimal<br />
LQG control is a linear function of the state. Finally, we showed the existence of critical arrival<br />
probabilities below which the optimal controller fails to<br />
stabilize the system. In this lecture we focus on UDP-like protocols. It turns out that when there is no feedback on whether a control packet has been delivered or not<br />
(e.g. UDP type protocols), the LQG optimal controller is in<br />
general nonlinear function of the information state. In the particular case where there is no measurement noise and the observation matrix C is invertible, we are able to show that the optimal controller is again linear, even if the separation principle still doesn't hold.<br />
Necessary conditions on the arrival probabilities for state boundedness are provided.<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-2_packet_based_control.pdf |Lecture: Packet-based Control]],<br />
For this lecture consider pages 71-88.<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/acc05.pdf Optimal Control with Unreliable Communication: the TCP Case], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. This is the paper where we published the results contained in the thesis</p><br />
<br />
<br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<br />
* [[Media:Nilsson_thesis_98.pdf | Real-Time Control Systems with Delays]], by Johan Nilsson, PhD Thesis.<br />
<br />
==Books==<br />
* <p> Stochastic Systems: Estimation, Identification and Adaptive Control, by P.R. Kumar, P. Varaiya, Prentice Hall, 1986. Difficult to find (Richard has a copy though). Even if it is not the most user friendly reading, chapters 6 to 8 contain a good reference for dynamic programming and LQG control.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529086/qid=1146074615/sr=2-2/ref=pd_bbs_b_2_2/103-1985563-9207029?s=books&v=glance&n=283155 Dynamic Programming and Optimal Control], by D. Bertsekas. </p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529108/qid=1146074615/sr=1-9/ref=sr_1_9/103-1985563-9207029?s=books&v=glance&n=283155 Neuro-Dynamic Programming], by D. Bertsekas and J. Tsitsiklis. </p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_Control:_the_TCP_caseNCS: Packet-based Control: the TCP case2006-04-28T07:44:47Z<p>Sinopoli: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture we consider the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We focus on the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon the results shown in the previous lecture on estimation with unreliable communication, we show the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.<br />
In the previous lectures we showed that, for protocols where<br />
packets are acknowledged at the receiver (e.g.\ TCP type<br />
protocols), the separation principle holds. Moreover, the optimal<br />
LQG control is a linear function of the state. Finally, we showed the existence of critical arrival<br />
probabilities below which the optimal controller fails to<br />
stabilize the system. In this lecture we focus on UDP-like protocols. It turns out that when there is no feedback on whether a control packet has been delivered or not<br />
(e.g. UDP type protocols), the LQG optimal controller is in<br />
general nonlinear function of the information state. In the particular case where there is no measurement noise and the observation matrix C is invertible, we are able to show that the optimal controller is again linear, even if the separation principle still doesn't hold.<br />
Necessary conditions on the arrival probabilities for state boundedness are provided.<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-2_packet_based_control.pdf |Lecture: Packet-based Control]],<br />
For this lecture consider pages 57-71.<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/acc05.pdf Optimal Control with Unreliable Communication: the TCP Case], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. This is the paper where we published the results contained in the thesis</p><br />
<br />
<br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<br />
* [[Media:Nilsson_thesis_98.pdf | Real-Time Control Systems with Delays]], by Johan Nilsson, PhD Thesis.<br />
<br />
==Books==<br />
* <p> Stochastic Systems: Estimation, Identification and Adaptive Control, by P.R. Kumar, P. Varaiya, Prentice Hall, 1986. Difficult to find (Richard has a copy though). Even if it is not the most user friendly reading, chapters 6 to 8 contain a good reference for dynamic programming and LQG control.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529086/qid=1146074615/sr=2-2/ref=pd_bbs_b_2_2/103-1985563-9207029?s=books&v=glance&n=283155 Dynamic Programming and Optimal Control], by D. Bertsekas. </p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529108/qid=1146074615/sr=1-9/ref=sr_1_9/103-1985563-9207029?s=books&v=glance&n=283155 Neuro-Dynamic Programming], by D. Bertsekas and J. Tsitsiklis. </p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_Control:_the_TCP_caseNCS: Packet-based Control: the TCP case2006-04-27T02:31:16Z<p>Sinopoli: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture we consider the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We focus on the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon the results shown in the previous lecture on estimation with unreliable communication, we show the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-2_packet_based_control.pdf |Lecture: Packet-based Control]],<br />
For this lecture consider pages 57-71.<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/acc05.pdf Optimal Control with Unreliable Communication: the TCP Case], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. This is the paper where we published the results contained in the thesis</p><br />
<br />
<br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<br />
* [[Media:Nilsson_thesis_98.pdf | Real-Time Control Systems with Delays]], by Johan Nilsson, PhD Thesis.<br />
<br />
==Books==<br />
* <p> Stochastic Systems: Estimation, Identification and Adaptive Control, by P.R. Kumar, P. Varaiya, Prentice Hall, 1986. Difficult to find (Richard has a copy though). Even if it is not the most user friendly reading, chapters 6 to 8 contain a good reference for dynamic programming and LQG control.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529086/qid=1146074615/sr=2-2/ref=pd_bbs_b_2_2/103-1985563-9207029?s=books&v=glance&n=283155 Dynamic Programming and Optimal Control], by D. Bertsekas. </p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529108/qid=1146074615/sr=1-9/ref=sr_1_9/103-1985563-9207029?s=books&v=glance&n=283155 Neuro-Dynamic Programming], by D. Bertsekas and J. Tsitsiklis. </p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=File:Nilsson_thesis_98.pdfFile:Nilsson thesis 98.pdf2006-04-27T02:28:54Z<p>Sinopoli: </p>
<hr />
<div></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Template:NCS:_Packet-based_Control:_the_TCP_case_NextTemplate:NCS: Packet-based Control: the TCP case Next2006-04-26T18:13:25Z<p>Sinopoli: </p>
<hr />
<div>NCS: Packet-based Control: the UDP case|Packet-based control UDP</div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Template:NCS:_Packet-based_Control:_the_TCP_case_PreviousTemplate:NCS: Packet-based Control: the TCP case Previous2006-04-26T18:11:50Z<p>Sinopoli: </p>
<hr />
<div>NCS: Packet-based Estimation|Packet-based Estimation</div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_Control:_the_TCP_caseNCS: Packet-based Control: the TCP case2006-04-26T18:09:05Z<p>Sinopoli: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture we consider the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We focus on the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon the results shown in the previous lecture on estimation with unreliable communication, we show the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-2_packet_based_control.pdf |Lecture: Packet-based Control]],<br />
For this lecture consider pages 57-71.<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/acc05.pdf Optimal Control with Unreliable Communication: the TCP Case], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. This is the paper where we published the results contained in the thesis</p><br />
<br />
<br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<br />
==Books==<br />
* <p> Stochastic Systems: Estimation, Identification and Adaptive Control, by P.R. Kumar, P. Varaiya, Prentice Hall, 1986. Difficult to find (Richard has a copy though). Even if it is not the most user friendly reading, chapters 6 to 8 contain a good reference for dynamic programming and LQG control.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529086/qid=1146074615/sr=2-2/ref=pd_bbs_b_2_2/103-1985563-9207029?s=books&v=glance&n=283155 Dynamic Programming and Optimal Control], by D. Bertsekas. </p><br />
<br />
* <p>[http://www.amazon.com/gp/product/1886529108/qid=1146074615/sr=1-9/ref=sr_1_9/103-1985563-9207029?s=books&v=glance&n=283155 Neuro-Dynamic Programming], by D. Bertsekas and J. Tsitsiklis. </p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=File:L5-2_packet_based_control.pdfFile:L5-2 packet based control.pdf2006-04-26T17:48:28Z<p>Sinopoli: </p>
<hr />
<div></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Template:NCS:_Packet-based_Estimation_NextTemplate:NCS: Packet-based Estimation Next2006-04-25T20:11:10Z<p>Sinopoli: </p>
<hr />
<div>NCS: Packet-based Control: the TCP case|Packet-based control TCP</div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_EstimationNCS: Packet-based Estimation2006-04-25T20:09:01Z<p>Sinopoli: /* Reading */</p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the effect of data loss on the performance of the Kalman filter for discrete-time linear systems. Observations are lost according to a bernoulli independent process, modeling this way the presence of a lossy networks between the sensors and the estimator. We first prove that the Kalman filter is still optimal in this new scenario.<br />
We then provide asymptotic results on the performance of the filter. In particular, we show that a transition from boundedness to instability arises if the arrival probability is lower that a critical value, that depends on the unstable eigenvalues of the system.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-1_packet_based_estimation.pdf |Lecture: Packet-based Estimation]]<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/tacs04.pdf Kalman Filtering with Intermittent Observations], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. Jordan and S. Sastry. This is the paper where all the proofs reside. Below I posted Chapter 3 of my thesis, which is essentially the same, but the notation is more consistent with the next two lectures.</p><br />
<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/NCS_class/optimal_estimation_lossy.pdf Optimal Estimation in Lossy Networks] This is chapter 3 of my thesis. Content is almost the same as the paper above, but notation is slightly modified to be consistent with the control part.</p><br />
<br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter], G. Welch and G. Bishop. A webpage with many links on Kalman filter.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from 1979. It contains a detailed mathematical presentation of filtering problems and the Kalman filter. A very good book.</p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Template:NCS:_Packet-based_Estimation_PreviousTemplate:NCS: Packet-based Estimation Previous2006-04-25T20:07:50Z<p>Sinopoli: </p>
<hr />
<div>Alice: Road Following|Alice RF</div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=Template:Alice:_Road_Following_NextTemplate:Alice: Road Following Next2006-04-25T20:07:04Z<p>Sinopoli: </p>
<hr />
<div>NCS: Packet-based Estimation|Packet-based Estimation</div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_EstimationNCS: Packet-based Estimation2006-04-25T20:03:07Z<p>Sinopoli: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the effect of data loss on the performance of the Kalman filter for discrete-time linear systems. Observations are lost according to a bernoulli independent process, modeling this way the presence of a lossy networks between the sensors and the estimator. We first prove that the Kalman filter is still optimal in this new scenario.<br />
We then provide asymptotic results on the performance of the filter. In particular, we show that a transition from boundedness to instability arises if the arrival probability is lower that a critical value, that depends on the unstable eigenvalues of the system.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-1_packet_based_estimation.pdf |Lecture: Packet-based Estimation]]<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/tacs04.pdf Kalman Filtering with Intermittent Observations], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. Jordan and S. Sastry. This is the paper where all the proofs reside. Below I posted Chapter 3 of my thesis, which is essentially the same, but the notation is more consistent with the next two lectures.</p><br />
<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/NCS_class/optimal_estimation_lossy.pdf Optimal Estimation in Lossy Networks] This is chapter of my thesis. Content is almost the same as the paper above, but notation is slightly modified to be consistent with the control part.</p><br />
<br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter], G. Welch and G. Bishop. A webpage with many links on Kalman filter.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from 1979. It contains a detailed mathematical presentation of filtering problems and the Kalman filter. A very good book.</p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_EstimationNCS: Packet-based Estimation2006-04-25T20:01:57Z<p>Sinopoli: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the effect of data loss on the performance of the Kalman filter for discrete-time linear systems. Observations are lost according to a bernoulli independent process, modeling this way the presence of a lossy networks between the sensors and the estimator. We first prove that the Kalman filter is still optimal in this new scenario.<br />
We then provide asymptotic results on the performance of the filter. In particular, we show that a transition from boundedness to instability arises if the arrival probability is lower that a critical value, that depends on the unstable eigenvalues of the system.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-1_packet_based_estimation.pdf |Lecture: Packet-based Estimation]]<br />
<br />
== Reading ==<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/tacs04.pdf Kalman Filtering with Intermittent Observations], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. Jordan and S. Sastry. This is the paper where all the proofs reside. Below I posted Chapter 3 of my thesis, which is essentially the same, but the notation is more consistent with the next two lectures.<br />
<br />
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/NCS_class/optimal_estimation_lossy.pdf Optimal Estimation in Lossy Networks] This is chapter of my thesis. Content is almost the same as the paper above, but notation is slightly modified to be consistent with the control part.</p><br />
<br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter], G. Welch and G. Bishop. A webpage with many links on Kalman filter.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from 1979. It contains a detailed mathematical presentation of filtering problems and the Kalman filter. A very good book.</p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_EstimationNCS: Packet-based Estimation2006-04-25T19:46:48Z<p>Sinopoli: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the effect of data loss on the performance of the Kalman filter for discrete-time linear systems. Observations are lost according to a bernoulli independent process, modeling this way the presence of a lossy networks between the sensors and the estimator. We first prove that the Kalman filter is still optimal in this new scenario.<br />
We then provide asymptotic results on the performance of the filter. In particular, we show that a transition from boundedness to instability arises if the arrival probability is lower that a critical value, that depends on the unstable eigenvalues of the system.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L5-1_packet_based_estimation.pdf |Lecture: Packet-based Estimation]]<br />
<br />
== Reading ==<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. A brief introduction to the Kalman filter in discrete time. No proofs are given, but it is a good first read.</p><br />
<br />
* <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter] A webpage that gives a proof and some applications.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html A New Approach to Linear Filtering and Prediction Problem], R.E. Kalman. ''Transactions of the ASME'', Series D, 1960. A classical paper. Still very readable. It uses different notation than the lecture, and present a different and more general proof. </p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter], G. Welch and G. Bishop. A webpage with many links on Kalman filter.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from 1979. It contains a detailed mathematical presentation of filtering problems and the Kalman filter. A very good book.</p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=File:L5-1_packet_based_estimation.pdfFile:L5-1 packet based estimation.pdf2006-04-25T19:45:48Z<p>Sinopoli: </p>
<hr />
<div></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=NCS:_Packet-based_EstimationNCS: Packet-based Estimation2006-04-25T19:38:13Z<p>Sinopoli: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the effect of data loss on the performance of the Kalman filter for discrete-time linear systems. Observations are lost according to a bernoulli independent process, modeling this way the presence of a lossy networks between the sensors and the estimator. We first prove that the Kalman filter is still optimal in this new scenario.<br />
We then provide asymptotic results on the performance of the filter. In particular, we show that a transition from boundedness to instability arises if the arrival probability is lower that a critical value, that depends on the unstable eigenvalues of the system.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L4-1_Kalman.pdf|Lecture: Kalman Filtering]]<br />
<br />
== Reading ==<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. A brief introduction to the Kalman filter in discrete time. No proofs are given, but it is a good first read.</p><br />
<br />
* <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter] A webpage that gives a proof and some applications.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html A New Approach to Linear Filtering and Prediction Problem], R.E. Kalman. ''Transactions of the ASME'', Series D, 1960. A classical paper. Still very readable. It uses different notation than the lecture, and present a different and more general proof. </p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter], G. Welch and G. Bishop. A webpage with many links on Kalman filter.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from 1979. It contains a detailed mathematical presentation of filtering problems and the Kalman filter. A very good book.</p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_270-2,_Spring_2006CDS 270-2, Spring 20062006-04-25T19:16:51Z<p>Sinopoli: </p>
<hr />
<div><table width="100%" cellspacing=0><br />
<tr valign=top><br />
<td rowspan=2 align=center> [[Image:citlogo.png|75px]]<br />
<td align=center><font color='blue' size='+2'>Networked Control Systems</font><br />
<td rowspan=2 align=center> [[Image:cdslogo.png|90px]]<br />
<tr valign=top><td align=center><font color='blue' size='+1'>Spring 2006</font><br />
</table><br />
<br />
<table align=right><tr><td>__TOC__</table><br />
<table cellspacing=0 cellpadding=0><br />
<tr valign=top><br />
<td width=60%><br />
* Instructor: [[User:Murray|Richard M. Murray]]<br />
* Co-instructors: [[User:Keviczky|Tamas Keviczky]], [[User:Mostofi|Yasi Mostofi]], [[User:Sandberg|Henrik Sandberg]], [[User:Sinopoli|Bruno Sinopoli]]<br />
<td align=center><br />
<table cellpadding=0 cellspacing=0><tr><td><br />
* [[Media:cds270-2_syllabus_sp06.pdf|Course syllabus]]<br />
* [http://listserv.cds.caltech.edu/mailman/listinfo/cds270 Course mailing list]<br />
* [[CDS 270: Information for Lecturers|Information for lecturers]]<br />
</table><br />
<tr><td colspan=2><br />
* Graduate instructors: Vijay Gupta, Zhipu Jin, Ling Shi, Demetri Spanos<br />
* Lectures: MWF 2-3 pm, 125 Steele<br />
</table><br />
<br />
== Course Schedule ==<br />
<br />
{| border=1 width=100%<br />
|-<br />
| Week || Date || Topic || Reading<br />
|-<br />
| align=center rowspan=5 | 1 <br />
| colspan=3 | '''Introduction to Networked Control Systems (R. Murray)'''<br />
|-<br />
| 27 Mar (M)<br />
| [[NCS: Introduction|Course overview, applications and administration]]<br />
| [[Media:cds270-2_syllabus_sp06.pdf|Syllabus]]; {{ncsbook|introduction|Ch 1}}<br />
|-<br />
| 29 Mar (W)<br />
| [[Alice: Introduction|Case study: Alice]]<br />
| [http://www.cds.caltech.edu/~murray/papers/2005t_cre+06-jfr.html Cremean et al, 2005]<br />
|-<br />
| colspan=3 | '''Networked embedded systems programming (R. Murray)'''<br />
|-<br />
| 31 Mar (F)<br />
| [[NCS: Message Transfer Systems|Message transfer systems: spread]]<br />
| {{ncsbook|embedded|Ch 2}}; [http://portal.acm.org/citation.cfm?id=359563 Lamport, 1978]<br />
|-<br />
| align=center rowspan=3 | 2<br />
| 3 Apr (M)<br />
| [[NCS: Multi-Threaded Control Systems|Multi-threaded control systems: pthreads]]<br />
| {{ncsbook|embedded|Ch 2}}; [http://www.llnl.gov/computing/tutorials/pthreads Pthreads]<br />
|-<br />
| 5 Apr (W)<br />
| [[Alice: Vehicle Control|Alice: adrive, astate, trajFollower]]<br />
| {{ncsbook|alice|App A}}; [http://gc.caltech.edu/wiki/index.php/Alice GCwiki]<br />
|-<br />
| 7 Apr* (F)<br />
| No class<br />
| <br />
|-<br />
| align=center rowspan=4 | 3<br />
| colspan=3 | '''Real-time trajectory generation and receding horizon control (R. Murray)'''<br />
|-<br />
| 10 Apr (M)<br />
| [[NCS: Real-Time Trajectory Generation|Real-time trajectory generation]]<br />
| {{ncsbook|trajgen|Ch 3}}<br />
|-<br />
| 12 Apr* (W)<br />
| [[NCS: Receding Horizon Control|Receding horizon control]] (T. Keviczky)<br />
| {{ncsbook|trajgen|Ch 3}}<br />
|-<br />
| 14 Apr (F)<br />
| [[Alice: Path Planning|Alice: plannerModule]]<br />
| {{ncsbook|alice|App A}}; [http://grandchallenge.caltech.edu/wiki/images/b/b3/Thesis.pdf Kogan, 2005]<br />
|-<br />
| align=center rowspan=4 | 4<br />
| colspan=3 | '''State estimation (H. Sandberg)'''<br />
|-<br />
| 17 Apr (M)<br />
| [[NCS: Kalman Filtering|Kalman filtering]]<br />
| {{ncsbook|estim|Ch 4}}; [http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf Welch and Bishop]<br />
|-<br />
| 19 Apr (W)<br />
| [[NCS: Moving Horizon Estimation|Moving horizon estimation]] <br />
| {{ncsbook|estim|Ch 4}}<br />
|-<br />
| 21 Apr (F) <br />
| [[Alice: Road Following|Alice: roadFollowing]] (L. Cremean)<br />
| {{ncsbook|alice|App A}}<br />
|-<br />
| align=center rowspan=4 | 5<br />
| colspan=3 | '''Packet-based estimation and control, I (B. Sinopoli)'''<br />
|-<br />
| 24 Apr (M)<br />
| [[NCS: Packet-based Estimation| Packet-based estimation]]<br />
| {{ncsbook|pack_estim|Ch 5}} <br />
|-<br />
| 26 Apr (W)<br />
| [[NCS: Packet-based Control: the TCP case|Packet-based Control: the TCP case]] <br />
| {{ncsbook|pack_cont|Ch 5}}<br />
|-<br />
| 28 Apr (F) <br />
| [[NCS: Packet-based Control: the TCP case|Packet-based Control: the UDP case]]<br />
| {{ncsbook|pack_cont2|Ch 5}}<br />
|-<br />
| align=center rowspan=4 | 6<br />
| colspan=3 | '''Packet-based estimation and control, II (L. Shi, Y. Mostofi)'''<br />
{{MWFrow|<br />
week=6|<br />
mondate=1 May*|montopic=|monreading=|<br />
weddate=3 May|wedtopic=|wedreading=|<br />
fridate=5 May|fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 7<br />
| colspan=3 | '''Distributed estimation and control (V. Gupta)'''<br />
{{MWFrow|<br />
week=7|<br />
mondate=8 May*|montopic=|monreading=|<br />
weddate=10 May*|wedtopic=|wedreading=|<br />
fridate=12 May |fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 8<br />
| colspan=3 | '''Cooperative control of multi-agent systems (Z. Jin, T. Keviczky)'''<br />
{{MWFrow|<br />
week=8|<br />
mondate=15 May|montopic=|monreading=|<br />
weddate=17 May*|wedtopic=|wedreading=|<br />
fridate=19 May|fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 9<br />
| colspan=3 | '''Project Presentations (All)'''<br />
{{MWFrow|<br />
week=9|<br />
mondate=22 May|montopic=No class|monreading=|<br />
weddate=24 May|wedtopic=Project presentations|wedreading=|<br />
fridate=26 May|fritopic=Project presentations|frireading=|<br />
}}<br />
|}<br />
<br />
== Course Description ==<br />
<br />
Increases in fast and inexpensive computing and communications have enabled a new generation information-rich control systems that rely on multi-threaded networked execution, distributed optimization, adaptation and learning, and contingency management in increasingly sophisticated ways. This course will describe a framework for building such systems and lay out some of the challenges to control theory that must be addressed to enable systematic design and analysis. Two examples will be used to illustrate the results and to serve as testbeds for course projects: [[Alice]], an autonomous vehicle that competed in the 2005 DARPA Grand<br />
Challenge and [[RoboFlag]], a robotic version of capture the flag. Key features of these systems include highly sensory-driven, information rich feedback systems, higher levels of decision making for goal and contingency management, and multi-threaded, networked control architectures.<br />
<br />
== Course Administration ==<br />
<br />
This course is a special topics course in which advanced students will prepare and present much of the lecture material. There is no required homework and no midterm or final exam. Course grades will be based on a course project.<br />
<br />
== Course Project ==<br />
<br />
All students in the course will demonstrate their knowledge of the material by analyzing or implementing a networked control system algorithm. Two testbeds are available for use by the class:<br />
<br />
* <p> '''[[Alice]]''' - Alice is an autonomous vehicle that was built by [http://team.caltech.edu Caltech undergraduates] to compete in the 2005 DARPA Grand Challenge. It is fully equipped with multiple terrain sensing cameras and LADARS, two GPS units and an inertial measurement unit (IMU) for measuring position and orientation, and 10 CPUs of computing horsepower inteconnected by a 1 Gb/s ethernet network. A module software architecture allows new functionality to be implemented and tested with relative ease. Requires knowledge of C/C++ programming under linux.</p><br />
<br />
* <p> '''[[RoboFlag]]''' - RoboFlag is a robotic version of capture the flag in which teams of 6-8 robots with 1-2 humans compete against a like team. A high fidelity simulator is available that allow full simulation of the dynamics, sensing and communications subsystems, providing realistic operation. Features include limited bitrate communication channels, limited sensor range for detecting opposing robots, and a graphical user interface for human-in-the-loop operation. Required knowlege of C/C++ program under Windows.</p><br />
<br />
'''Project ideas''' (will be expanded during the term)<br />
* Benchmark the performance of different messaging protocols (eg, broadcast, UDP, TCP) for communicating the state and terrain data on Alice<br />
* Implement and analyze the effect of "shock absobers" (control buffers, state estimators) on RoboFlag<br />
* Implement state estimation and/or multi-description coding on Alice to handle lost packets of terrain data<br />
<br />
<span id=archive /><br />
<br />
[[Category:Courses]] [[Category:2005-06 Courses]]</div>Sinopolihttp://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_270-2,_Spring_2006CDS 270-2, Spring 20062006-04-25T19:15:42Z<p>Sinopoli: </p>
<hr />
<div><table width="100%" cellspacing=0><br />
<tr valign=top><br />
<td rowspan=2 align=center> [[Image:citlogo.png|75px]]<br />
<td align=center><font color='blue' size='+2'>Networked Control Systems</font><br />
<td rowspan=2 align=center> [[Image:cdslogo.png|90px]]<br />
<tr valign=top><td align=center><font color='blue' size='+1'>Spring 2006</font><br />
</table><br />
<br />
<table align=right><tr><td>__TOC__</table><br />
<table cellspacing=0 cellpadding=0><br />
<tr valign=top><br />
<td width=60%><br />
* Instructor: [[User:Murray|Richard M. Murray]]<br />
* Co-instructors: [[User:Keviczky|Tamas Keviczky]], [[User:Mostofi|Yasi Mostofi]], [[User:Sandberg|Henrik Sandberg]], [[User:Sinopoli|Bruno Sinopoli]]<br />
<td align=center><br />
<table cellpadding=0 cellspacing=0><tr><td><br />
* [[Media:cds270-2_syllabus_sp06.pdf|Course syllabus]]<br />
* [http://listserv.cds.caltech.edu/mailman/listinfo/cds270 Course mailing list]<br />
* [[CDS 270: Information for Lecturers|Information for lecturers]]<br />
</table><br />
<tr><td colspan=2><br />
* Graduate instructors: Vijay Gupta, Zhipu Jin, Ling Shi, Demetri Spanos<br />
* Lectures: MWF 2-3 pm, 125 Steele<br />
</table><br />
<br />
== Course Schedule ==<br />
<br />
{| border=1 width=100%<br />
|-<br />
| Week || Date || Topic || Reading<br />
|-<br />
| align=center rowspan=5 | 1 <br />
| colspan=3 | '''Introduction to Networked Control Systems (R. Murray)'''<br />
|-<br />
| 27 Mar (M)<br />
| [[NCS: Introduction|Course overview, applications and administration]]<br />
| [[Media:cds270-2_syllabus_sp06.pdf|Syllabus]]; {{ncsbook|introduction|Ch 1}}<br />
|-<br />
| 29 Mar (W)<br />
| [[Alice: Introduction|Case study: Alice]]<br />
| [http://www.cds.caltech.edu/~murray/papers/2005t_cre+06-jfr.html Cremean et al, 2005]<br />
|-<br />
| colspan=3 | '''Networked embedded systems programming (R. Murray)'''<br />
|-<br />
| 31 Mar (F)<br />
| [[NCS: Message Transfer Systems|Message transfer systems: spread]]<br />
| {{ncsbook|embedded|Ch 2}}; [http://portal.acm.org/citation.cfm?id=359563 Lamport, 1978]<br />
|-<br />
| align=center rowspan=3 | 2<br />
| 3 Apr (M)<br />
| [[NCS: Multi-Threaded Control Systems|Multi-threaded control systems: pthreads]]<br />
| {{ncsbook|embedded|Ch 2}}; [http://www.llnl.gov/computing/tutorials/pthreads Pthreads]<br />
|-<br />
| 5 Apr (W)<br />
| [[Alice: Vehicle Control|Alice: adrive, astate, trajFollower]]<br />
| {{ncsbook|alice|App A}}; [http://gc.caltech.edu/wiki/index.php/Alice GCwiki]<br />
|-<br />
| 7 Apr* (F)<br />
| No class<br />
| <br />
|-<br />
| align=center rowspan=4 | 3<br />
| colspan=3 | '''Real-time trajectory generation and receding horizon control (R. Murray)'''<br />
|-<br />
| 10 Apr (M)<br />
| [[NCS: Real-Time Trajectory Generation|Real-time trajectory generation]]<br />
| {{ncsbook|trajgen|Ch 3}}<br />
|-<br />
| 12 Apr* (W)<br />
| [[NCS: Receding Horizon Control|Receding horizon control]] (T. Keviczky)<br />
| {{ncsbook|trajgen|Ch 3}}<br />
|-<br />
| 14 Apr (F)<br />
| [[Alice: Path Planning|Alice: plannerModule]]<br />
| {{ncsbook|alice|App A}}; [http://grandchallenge.caltech.edu/wiki/images/b/b3/Thesis.pdf Kogan, 2005]<br />
|-<br />
| align=center rowspan=4 | 4<br />
| colspan=3 | '''State estimation (H. Sandberg)'''<br />
|-<br />
| 17 Apr (M)<br />
| [[NCS: Kalman Filtering|Kalman filtering]]<br />
| {{ncsbook|estim|Ch 4}}; [http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf Welch and Bishop]<br />
|-<br />
| 19 Apr (W)<br />
| [[NCS: Moving Horizon Estimation|Moving horizon estimation]] <br />
| {{ncsbook|estim|Ch 4}}<br />
|-<br />
| 21 Apr (F) <br />
| [[Alice: Road Following|Alice: roadFollowing]] (L. Cremean)<br />
| {{ncsbook|alice|App A}}<br />
|-<br />
| align=center rowspan=4 | 5<br />
| colspan=3 | '''Packet-based estimation and control, I (B. Sinopoli)'''<br />
|-<br />
| 24 Apr (M)<br />
| [[NCS: Packet-based Estimation| packet-based estimation]]<br />
| {{ncsbook|pack_estim|Ch 5}}; <br />
|-<br />
| 26 Apr (W)<br />
| [[NCS: Packet-based Control: the TCP case|Packet-based Control: the TCP case]] <br />
| {{ncsbook|pack_cont|Ch 5}}<br />
|-<br />
| 28 Apr (F) <br />
| [[NCS: Packet-based Control: the TCP case|Packet-based Control: the UDP case]]<br />
| {{ncsbook|pack_cont2|Ch 5}}<br />
|-<br />
| align=center rowspan=4 | 6<br />
| colspan=3 | '''Packet-based estimation and control, II (L. Shi, Y. Mostofi)'''<br />
{{MWFrow|<br />
week=6|<br />
mondate=1 May*|montopic=|monreading=|<br />
weddate=3 May|wedtopic=|wedreading=|<br />
fridate=5 May|fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 7<br />
| colspan=3 | '''Distributed estimation and control (V. Gupta)'''<br />
{{MWFrow|<br />
week=7|<br />
mondate=8 May*|montopic=|monreading=|<br />
weddate=10 May*|wedtopic=|wedreading=|<br />
fridate=12 May |fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 8<br />
| colspan=3 | '''Cooperative control of multi-agent systems (Z. Jin, T. Keviczky)'''<br />
{{MWFrow|<br />
week=8|<br />
mondate=15 May|montopic=|monreading=|<br />
weddate=17 May*|wedtopic=|wedreading=|<br />
fridate=19 May|fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 9<br />
| colspan=3 | '''Project Presentations (All)'''<br />
{{MWFrow|<br />
week=9|<br />
mondate=22 May|montopic=No class|monreading=|<br />
weddate=24 May|wedtopic=Project presentations|wedreading=|<br />
fridate=26 May|fritopic=Project presentations|frireading=|<br />
}}<br />
|}<br />
<br />
== Course Description ==<br />
<br />
Increases in fast and inexpensive computing and communications have enabled a new generation information-rich control systems that rely on multi-threaded networked execution, distributed optimization, adaptation and learning, and contingency management in increasingly sophisticated ways. This course will describe a framework for building such systems and lay out some of the challenges to control theory that must be addressed to enable systematic design and analysis. Two examples will be used to illustrate the results and to serve as testbeds for course projects: [[Alice]], an autonomous vehicle that competed in the 2005 DARPA Grand<br />
Challenge and [[RoboFlag]], a robotic version of capture the flag. Key features of these systems include highly sensory-driven, information rich feedback systems, higher levels of decision making for goal and contingency management, and multi-threaded, networked control architectures.<br />
<br />
== Course Administration ==<br />
<br />
This course is a special topics course in which advanced students will prepare and present much of the lecture material. There is no required homework and no midterm or final exam. Course grades will be based on a course project.<br />
<br />
== Course Project ==<br />
<br />
All students in the course will demonstrate their knowledge of the material by analyzing or implementing a networked control system algorithm. Two testbeds are available for use by the class:<br />
<br />
* <p> '''[[Alice]]''' - Alice is an autonomous vehicle that was built by [http://team.caltech.edu Caltech undergraduates] to compete in the 2005 DARPA Grand Challenge. It is fully equipped with multiple terrain sensing cameras and LADARS, two GPS units and an inertial measurement unit (IMU) for measuring position and orientation, and 10 CPUs of computing horsepower inteconnected by a 1 Gb/s ethernet network. A module software architecture allows new functionality to be implemented and tested with relative ease. Requires knowledge of C/C++ programming under linux.</p><br />
<br />
* <p> '''[[RoboFlag]]''' - RoboFlag is a robotic version of capture the flag in which teams of 6-8 robots with 1-2 humans compete against a like team. A high fidelity simulator is available that allow full simulation of the dynamics, sensing and communications subsystems, providing realistic operation. Features include limited bitrate communication channels, limited sensor range for detecting opposing robots, and a graphical user interface for human-in-the-loop operation. Required knowlege of C/C++ program under Windows.</p><br />
<br />
'''Project ideas''' (will be expanded during the term)<br />
* Benchmark the performance of different messaging protocols (eg, broadcast, UDP, TCP) for communicating the state and terrain data on Alice<br />
* Implement and analyze the effect of "shock absobers" (control buffers, state estimators) on RoboFlag<br />
* Implement state estimation and/or multi-description coding on Alice to handle lost packets of terrain data<br />
<br />
<span id=archive /><br />
<br />
[[Category:Courses]] [[Category:2005-06 Courses]]</div>Sinopoli