Difference between revisions of "Supplement: Optimization-Based Control"

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{{supheader|Optimization-Based Control}}
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<font size="+1">Richard M. Murray (Caltech)</font>
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These notes serve as a supplement to ''Feedback Systems'' by {{Astrom}} and Murray and expand on some of the topics introduced there.  Our focus is on the use of optimization-based methods for control, including optimal control theory, receding horizon control and Kalman filtering.  Each chapter is intended to be a standalone reference for advanced topics that are introduced in ''Feedback Systems''.
 
These notes serve as a supplement to ''Feedback Systems'' by {{Astrom}} and Murray and expand on some of the topics introduced there.  Our focus is on the use of optimization-based methods for control, including optimal control theory, receding horizon control and Kalman filtering.  Each chapter is intended to be a standalone reference for advanced topics that are introduced in ''Feedback Systems''.
  
* Chapter 1: {{am05pdf|obc08-trajgen|26Jan08|Trajectory Generation and Tracking}}
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'''Note:''' These notes are in draft form and may contain errors.  Permission is granted to download and print a copy for individual use, but this material may not be reproduced, in whole or in part, without written consent from the author.
* Chapter 2: {{am05pdf|obc08-optimal|26Jan08|Optimal Control}}
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* Chapter 3: {{am05pdf|obc08-rhc|30Jan08|Receding Horizon Control}}
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{{OBC quick links}}
* Chapter 4: {{am05pdf|obc08-stochastic|19Feb08|Stochastic Systems}}
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===== News ([[OBC:Archived news|archive]]) =====
* Chapter 5: {{am05pdf|obc08-kalman|23Feb08|Kalman Filtering}} (pretty rough)
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* 15 Feb 10: updated version of Chapter 4 (stochastic systems) is posted; multiple fixes + some new material
* Chapter 6: {{am05pdf|obc08-fusion|28Feb08|Sensor Fusion}} (bare bones)
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* 3 Jan 10: posted updated version of Chapters 1 and 2 (mainly small fixes) + working errata link
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* 22 Dec 09: updated versions of all chapters posted; working through small fixes over the next few weeks
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* 22 Dec 09: updated supplement main page to a new format
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* 4 Jan 09: Version 2.0b posted - fixes and error corrections for chapters 1-4
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<p>
  
=== Summary of Changes ===
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=== Contents ===
* 1 Jun 08: Version 2.0a - fixes and updates throughout; posting individual chapters as they are done
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{| width=100% border=1  
* 27 Feb 08: Version 1.8a - initial cut at discrete-time/sensor fusion chapter; bare bones derivations
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|- valign=top
* 23 Feb 08: Version 1.7b - fixed up the Kalman filtering notes a bit, but they still need more work.  Inserted MATLAB code as an example of how to apply everything
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| width=50% |
* 21 Feb 08: Version 1.7a - first version of Kalman filtering notes; still pretty rough (bullets instead of paragraphs)
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* {{OBC pdf|Contents and Preface|obc-frontmatter|03Jan10}}
* 15 Feb 08: Version 1.6d - added references for further reading + summary figure
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* {{OBC pdf|Ch 1 - Trajectory Generation and Tracking|obc-trajgen|03Jan10}}
* 13 Feb 08: Version 1.6c - use R_V instead of Q_V (consistent with main text)
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** Two Degree of Freedom Design
* 12 Feb 08: Version 1.6b posted; updated state space computations for stochastic systems
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** Trajectory Tracking and Gain Scheduling
* 11 Feb 08: Version 1.6a posted; new chapter on stochastic systems
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** Trajectory Generation and Differential Flatness
* 30 Jan 08: Version 1.4a posted; new chapter on receding horizon control
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* {{OBC pdf|Ch 2 - Optimal Control|obc-optimal|27Oct18}}
* 25 Jan 08: fixed up some bad references; expanded the LQR design example (pvtol); added example of abnormal extremal
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** Review: Optimization
* 23 Jan 08: updated Ch 2; more details on LQR
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** Optimal Control of Systems
* 14 Jan 08: updated Ch 1 and posted Ch 2.  Fixed a couple of small bugs in Ch 1.  Changed <math>u_{ff}</math> to <math>u_d</math>.
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** Examples
* 7 Jan 08: first post (Ch 1)
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** Linear Quadratic Regulators
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** Choosing LQR Weights
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** Advanced Topics
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* {{OBC pdf|Ch 3 - Receding Horizon Control|obc-rhc|22Dec09}}
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** Optimization-Based Control
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** Receding Horizon Control with CLF Terminal Cost
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** Receding Horizon Control Using Differential Flatness
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** Implementation on the Caltech Ducted Fan
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| width=50% |
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* {{OBC pdf|Ch 4 - Stochastic Systems|obc-stochastic|15Feb10}}
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** Review of Random Variables
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** Introduction to Random Processes
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** Continuous-Time, Vector-Valued Random Processes
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** Linear Stochastic Systems
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** Random Processes in the Frequency Domain
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* {{OBC pdf|Ch 5 - Kalman Filtering|obc-kalman|22Dec09}}
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** Linear Quadratic Estimators
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** Extensions of the Kalman Filter
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** LQG Control
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** Application to a Vectored Thrust Aircraft
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* {{OBC pdf|Ch 6 - Sensor Fusion|obc-fusion|22Dec09}}
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** Discrete-Time Stochastic Systems
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** Kalman Filters in Discrete Time
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** Predictor-Corrector Form
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** Sensor Fusion
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** Information Filters
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** Additional Topics
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* {{OBC pdf|Bibliography and Index|obc-backmatter|15Feb10}}
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|}

Latest revision as of 19:43, 27 October 2018

Richard M. Murray (Caltech)

These notes serve as a supplement to Feedback Systems by Åström and Murray and expand on some of the topics introduced there. Our focus is on the use of optimization-based methods for control, including optimal control theory, receding horizon control and Kalman filtering. Each chapter is intended to be a standalone reference for advanced topics that are introduced in Feedback Systems.

Note: These notes are in draft form and may contain errors. Permission is granted to download and print a copy for individual use, but this material may not be reproduced, in whole or in part, without written consent from the author.

Quick Links
News (archive)
  • 15 Feb 10: updated version of Chapter 4 (stochastic systems) is posted; multiple fixes + some new material
  • 3 Jan 10: posted updated version of Chapters 1 and 2 (mainly small fixes) + working errata link
  • 22 Dec 09: updated versions of all chapters posted; working through small fixes over the next few weeks
  • 22 Dec 09: updated supplement main page to a new format
  • 4 Jan 09: Version 2.0b posted - fixes and error corrections for chapters 1-4

Contents

  • Contents and Preface (PDF, 03Jan10)
  • Ch 1 - Trajectory Generation and Tracking (PDF, 03Jan10)
    • Two Degree of Freedom Design
    • Trajectory Tracking and Gain Scheduling
    • Trajectory Generation and Differential Flatness
  • Ch 2 - Optimal Control (PDF, 27Oct18)
    • Review: Optimization
    • Optimal Control of Systems
    • Examples
    • Linear Quadratic Regulators
    • Choosing LQR Weights
    • Advanced Topics
  • Ch 3 - Receding Horizon Control (PDF, 22Dec09)
    • Optimization-Based Control
    • Receding Horizon Control with CLF Terminal Cost
    • Receding Horizon Control Using Differential Flatness
    • Implementation on the Caltech Ducted Fan
  • Ch 4 - Stochastic Systems (PDF, 15Feb10)
    • Review of Random Variables
    • Introduction to Random Processes
    • Continuous-Time, Vector-Valued Random Processes
    • Linear Stochastic Systems
    • Random Processes in the Frequency Domain
  • Ch 5 - Kalman Filtering (PDF, 22Dec09)
    • Linear Quadratic Estimators
    • Extensions of the Kalman Filter
    • LQG Control
    • Application to a Vectored Thrust Aircraft
  • Ch 6 - Sensor Fusion (PDF, 22Dec09)
    • Discrete-Time Stochastic Systems
    • Kalman Filters in Discrete Time
    • Predictor-Corrector Form
    • Sensor Fusion
    • Information Filters
    • Additional Topics
  • Bibliography and Index (PDF, 15Feb10)