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## List of results

•   +
• <h3>Abstract</h3> This work de
<h3>Abstract</h3> This work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the point of view of Lagrangian mechanics and with a view to control theoretical applications. The basic methodology is that of geometric mechanics emphasizing the formulation of Lagrange d'Alembert with the use of connections and momentum maps associated with the given symmetry group. We begin by recalling and extending the results of Koiller from the case of principal connections to the general Ehresmann case. Unlike the situation with standard configuration space constraints, the symmetry in the nonholonomic case may or may not lead to conservation laws. In any case, the momentum map determined by the symmetry group satisfies a useful differential equation that decouples from the group variables. This momentum equation is shown to have the form of a covariant derivative of the momentum equal to a component of the internal generalized force. An alternative description using a "body reference frame" realizes part of the momentum equation as those components of the Euler-Poincare equations along the symmetry directions consistent with the constraints. One of the purposes of this paper is to derive this evolution equation for the momentum and to distinguish geometrically and mechanically the cases where it is conserved and those where it is not. An example of the former is a ball or vertical disk rolling on a flat plane and an example of the latter is the snakeboard, a modified version of the skateboard which uses momentum coupling for locomotion generation. We construct a synthesis of the mechanical connection and the Ehresmann connection defining the constraints, obtaining an important new object, the nonholonomic connection. Under conditions that include the Chaplygin case (we use the terminology "purely kinematic") and the case in which the momentum is conserved, it is known that one can perform a reduction similar to Lagrangian reduction, which includes the Routh procedure. We generalize this reduction procedure to the case in which the nonholonomic connection is a principal connection for the given symmetry group; this case includes all of the examples considered in the paper and many others as well, such as the wobblestone, the nonvertical disk and the bicycle. Another purpose of this work is to lay the foundation for future work on mechanical systems with control so that one can adapt well developed techniques from holonomic systems, such as constructive controllability and geometric phases. Although this will be the subject of future work, the methodology of the present paper is developed with these goals in mind.
per is developed with these goals in mind.  +
• <p>This paper describes a technique for performing model reduction of systems with travelling wave solutions via a Karhunen Loeve framework.  +
• A cascade discrete-continuous state estima
A cascade discrete-continuous state estimator design is presented for a class of monotone systems with both continuous and discrete state evolution. The proposed estimator exploits the partial order preserved by the system dynamics in order to satisfy two properties. First, its computation complexity scales with the number of variables to be estimated instead of scaling with the size of the discrete state space. Second, a separation principle holds: the continuous state estimation error is bounded by a monotonically decreasing function of the discrete state estimation error, the latter one converging to zero. A multi-robot example is proposed.
o zero. A multi-robot example is proposed.  +
• A central goal of synthetic biology is to
A central goal of synthetic biology is to engineer cellular behavior by engineering synthetic gene networks for a variety of biotechnology and medical applications. The process of engineering gene networks often involves an iterative âdesign-build-testâ cycle, whereby the parts and connections that make up the network are built, characterized and varied until the desired network function is reached. Many advances have been made in the design and build portions of this cycle. However, the slow process of in vivo characterization of network function often limits the timescale of the testing step. Cell-free transcription-translation (TX-TL) systems offer a simple and fast alternative to performing these characterizations in cells. Here we provide an overview of a cell-free TX-TL system that utilizes the native Escherichia coli TX-TL machinery, thereby allowing a large repertoire of parts and networks to be characterized. As a way to demonstrate the utility of cell-free TX-TL, we illustrate the characterization of two genetic networks: an RNA transcriptional cascade and a protein regulated incoherent feed-forward loop. We also provide guidelines for designing TX-TL experiments to characterize new genetic networks. We end with a discussion of current and emerging applications of cell free systems.
merging applications of cell free systems.  +
• A community of genetically heterogeneous c
A community of genetically heterogeneous cells embedded in an unmixed medium allows for sophisticated operations by retaining spatial differentiation and coordinating division-of-labor. To establish the principles of engineering reliable cell-cell communication in a heterogeneous environment, we examined how circuit parameters and spatial placement affect the range of length and time scales over which simple communication circuits interact. We constructed several "sender" and "receiver" strains with quorum-sensing signaling circuits. The sender cell colony produces acyl homoserine lactones (AHL), which diffuse across the semisolid medium. The receiver cell colony detects these signal molecules and reports by fluorescence. We have found that a single colony of one sender variant is sufficient to induce receiver response at more than 1.5cm separation. Furthermore, AHL degradase expression in receiver colonies produces a signal threshold effect and reduces the response level in subsequent receiver colonies. Finally, our investigation on the spatial placement of colonies gave rise to the design of a multicellular long-range communication array consisting of two alternating colony types. Its signal response successfully propagated colony-by-colony along a six-colony array spanning 4.8cm at a transmission velocity of 12.8 hours per colony or 0.075cm per hour. In addition, we have developed a reaction-diffusion model that recreates the observed behaviors of the many performed experiments using data-informed parameter estimates of signal diffusion, gene expression, and nutrient consumption. These results demonstrate that a mixed community of colonies can enable new patterning programs, and the corresponding model will facilitate the rational design of complex communication networks.
design of complex communication networks.  +
• A computational approach to generate real-
A computational approach to generate real-time, optimal trajectories for a flight control experiment is presented. Minimum time trajectories are computed for hover-to-hover and forward flight maneuvers. Instantaneous changes in the trajectory constraints that model obstacles and threats are also investigated. Experimental results using the Nonlinear Trajectory Generation software package show good closed loop performance for both maneuvers and in the presence of obstacles. Success of the algorithm demonstrates that high-conﬁdence real-time trajectory generation is achievable in spite of the highly nonlinear and non-convex nature of the problem.
near and non-convex nature of the problem.  +
• A computational approach to generating agg
A computational approach to generating aggressive trajectories in real-time for constrained mechanical systems is presented. The algorithm is based on a combination of nonlinear control theory, spline theory, and sequential quadratic programming. It is demonstrated that real-time trajectory generation for constrained mechanical systems is possible by mapping the problem to one of finding trajectory curves in a lower dimensional space. Performance of the algorithm is compared with existing optimal trajectory generation techniques. Numerical results are reported using the NTG software package.
reported using the NTG software package.  +
• A computationally efficient technique for
A computationally efficient technique for the numerical solution of optimal control problems is discussed. This method utilizes tools from nonlinear control theory to transform the optimal control problem to a new, lower dimensional set of coordinates. It is hypothesized that maximizing the relative degree is directly related to minimizing the computation time. Firm evidence of this hypothesis is given. Results are presented using the Nonlinear Trajectory Generation (NTG) software package.
jectory Generation (NTG) software package.  +
• A computationally e±cient technique for th
A computationally e±cient technique for the numerical solution of constrained optimal control problems governed by one-dimensional partial differential equations is considered in this paper. This technique utilizes inversion to map the optimal control problem to a lower dimensional space. Results are presented using the Nonlinear Trajectory Generation software package (NTG) showing that real-time implementation may be possible.
real-time implementation may be possible.  +
• A cooperative control system consists of m
A cooperative control system consists of multiple, autonomous components interacting to<br /> control their environment. Examples include air tra±c control systems, automated factories,<br /> robot soccer teams and sensor/actuator networks. Designing such systems requires a combination of tools from control theory and distributed systems. In this article, we review some of these tools and then focus on the Computation and Control Language, CCL, which we have developed as a modeling tool and a programming language for cooperative control systems.
language for cooperative control systems.  +
• A feedback controller closes the loop from vision to wing motion to stabilize forward flight in a simulation of Drosophila Melanogaster.  +
• A generalized model predictive control (MP
A generalized model predictive control (MPC) formulation is derived that extends the existing theory to a multi-vehicle formation stabilization problem. The vehicles are individually governed by nonlinear and constrained dynamics. The extension considers formation stabilization to a set of permissible equilibria, rather than a unique equilibrium. Simulations for three vehicle formations with input constrained dynamics on con¯guration space SE(2) are performed using a nonlinear trajectory generation (NTG) software package developed at Caltech. Preliminary results and an outline of future work for scaling/decentralizing the MPC approach and applying it to an emerging experimental testbed are given.
n emerging experimental testbed are given.  +
• A master equation describes the continuous
A master equation describes the continuous-time evolution of a probability distribution, and is characterized by a simple bilinear structure and an often-high dimension. We develop a model reduction approach in which the number of possible confiurations and corresponding dimension is reduced, by removing improbable configurations and grouping similar ones. Error bounds for the reduction are derived based on a minimum and maximum time scale of interest. An analogous linear identification procedure is then presented, which computes the state and output matrices for a predetermined configuration set. These ideas are demonstrated first in a finite-dimensional model inspired by problems in surface evolution, and then in an infinite- dimensional film growth master equation.
- dimensional film growth master equation.  +
• A new technique for stabilizing nonholonom
A new technique for stabilizing nonholonomic systems to trajectories is presented. It is well known that such systems cannot be stabilized to a point using smooth static state feedback. In this paper we suggest the use of control laws for stabilizing a system about a trajectory, instead of a point. Given a nonlinear system and a desired (nominal) feasible trajectory, the paper gives an explicit control law which will locally exponentially stabilize the system to the desired trajectory. The theory is applied to several examples, including a car-like robot.
eral examples, including a car-like robot.  +
• A numerical algorithm for computing necess
A numerical algorithm for computing necessary conditions for performance specifications is developed for nonlinear uncertain systems. The algorithm is similar in nature and behavior to the power algorithm for the mu lower bound, and doesn't rely on a descent method. The algorithm is applied to a practical example.
gorithm is applied to a practical example.  +
• A reactive safety mode is built into a rob
A reactive safety mode is built into a robust model predictive control algorithm for uncertain nonlinear systems with bounded disturbances. The algorithm enforces state and control constraints and blends two modes: (I) standard, guarantees re-solvability and asymptotic convergence in a robust receding-horizon manner; (II) safety, if activated, guarantees containment within an invariant set about a reference. The reactive safety mode provides robustness to unexpected, but real-time anticipated, state-constraint changes during standard mode operation. The safety-mode control policy is designed offline and can be activated at any arbitrary time. The standard-mode control has feedforward and feedback components: feedforward is from online solution of a finite-horizon optimal control problem; feedback is designed offline to provide robustness to system uncertainty and disturbances and to establish an invariant âstate tubeâ that guarantees standard-mode re-solvability at any time. The algorithm design is shown for a class of systems with incrementally-conic uncertain/nonlinear terms and bounded disturbances.
/nonlinear terms and bounded disturbances.  +
• A reactor for the deposition of supercondu
A reactor for the deposition of superconducting \ybcolong\;thin films is modeled and studied from a control perspective to determine the heat transfer dynamics of the reactor under active thermal control. A nonlinear wavelength-dependent heat transfer model is developed to predict reactor heat transfer throughout the film growth process, and preliminary component testing is conducted to validate the model. The model is linearized about a typical operating point and analyzed with linear feedback control methods to determine the performance of the reactor under observer-based feedback control with film growth disturbances. The controller and observer are selected through linear quadratic regulator and linear quadratic estimator methods. Rates of convergence of the controller and observer are determined through examination of the eigenvalues of the linearized system, and disturbance rejection is assessed with ${\mathcal H}_2$ and ${\mathcal H}_\infty$ norms. The eigenvalue and norm analysis is applied to varying reactor design parameters to quantify performance tradeoffs. The maximum errors associated with control and with estimation of a nominal design case are both 21 K, and the longest time scales are 45 seconds and 10 seconds for the controller and observer, respectively.
the controller and observer, respectively.  +
• A synthetic cell-cell signaling circuit sh
A synthetic cell-cell signaling circuit should ideally be (1) metabolically lightweight, (2) insulated from endogenous gene networks, and (3) excitable rather than oscillatory or bistable. To accomplish these three features, we propose a synchronized pulse-generating circuit based on the design of published synchronized oscillators. This communication module employs a pulse generator built using Lux-type quorum sensing components and an IFFL transcriptional circuit. Both the input and output of this module are AHLs, the quorum sensing signaling molecule. Cells bearing this module therefore act as an excitable medium, producing a pulse of AHL when stimulated by exogenous AHL. Using simulation and microscopy, we demonstrate how this circuit enables traveling pulses of AHL production through microcolonies growing in two dimensions. Traveling pulses achieve cell-cell communication at longer distances than can be achieved by diffusion of signal from sender to receiver cells and may permit more sophisticated coordination in synthetic consortia.
cated coordination in synthetic consortia.  +
• AbstractIn this paper, we consider the pr
AbstractIn this paper, we consider the problem of optimal Linear Quadratic Gaussian control of a system in which communication between the sensor and the controller occurs across a packet-dropping link. We first prove a separation principle that allows us to solve this problem using a standard LQR state-feedback design, along with an optimal algorithm for propagating and using the information across the unreliable link. Then we present one such optimal algorithm, which consists of a Kalman filter at the sensor side of the link, and a switched linear filter at the controller side. Our design does not assume any statistical model of the packet drop events, and is thus optimal for any arbitrary packet drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design.
ication of an existing LQG control design.  +
• AbstractWe examine the problem of distrib
AbstractWe examine the problem of distributed estimation when only one sensor can take a measurement per time step. We solve for the optimal recursive estimation algorithm when the sensor switching schedule is given. We then consider the effect of noise in communication channels. We also investigate the problem of determining an optimal sensor switching strategy. We see that this problem involves searching a tree in general and propose two strategies for pruning the tree to minimize the computation. The first is a sliding window strategy motivated by the Viterbi algorithm, and the second one uses thresholding. The performance of the algorithms is illustrated using numerical examples.
s is illustrated using numerical examples.  +
• AbstractâIn this paper, we consider a st
AbstractâIn this paper, we consider a state estimation problem over a bandwidth limited network. A sensor network consisting of N sensors is used to observe the states of M plants, but only p Â· N sensors can transmit their measurements to a centralized estimator at each time. Therefore a suitable scheme that schedules the proper sensors to access the network at each time so that the total estimation error is minimized is required. We propose four different sensor scheduling schemes. The static and stochastic schemes assume no feedback from the estimator to the scheduler, while the two dynamic schemes, Maximum Error First (MEF) and Maximum Deduction First (MDF) assume such feedback is available. We compare the four schemes via some examples and show MEF and MDF schemes are better than the static and stochastic schemes, which demonstrates that feedback can play an important role in this remote state estimation problem. We also show that MDF is better than MEF as MDF considers the total estimation error while MEF considers the individual estimation error.
considers the individual estimation error.  +
• Accelerating the pace of synthetic biology
Accelerating the pace of synthetic biology experiments requires new approaches for rapid prototyping of circuits from individual DNA regulatory elements. However, current testing standards require days to weeks due to cloning and in vivo transformation. In this work, we first characterized methods to protect linear DNA strands from exonuclease degradation in an Escherichia coli based transcription-translation cell-free system (TX-TL), as well as mechanisms of degradation. This enables the use of linear DNA PCR products in TX-TL. We then explored methods to calibrate linear DNA to plasmid DNA by concentration. We also demonstrated assembly technology to rapidly build circuits entirely in vitro from separate parts. Using this strategy, we prototyped a four-piece genetic switch in under 8 hours entirely in vitro. Rapid in vitro assembly has applications for prototyping circuits of unlimited size when combined with predictive computational models.
ined with predictive computational models.  +
• Active control of rotating stall and surge
Active control of rotating stall and surge using bleed valves has been demonstrated on low and high speed compressors using high bandwidth actuators. In this paper we provide a method to reduce the bandwidth and rate requirements for control of rotating stall by combining an axisymmetric bleed valve with continuous air injection. The addition of the continuous air injection is modeled as a shift of both the stable and unstable parts of the compressor characteristic and serves to reduce the requirement of a bleed valve used for rotating stall stabilization purpose. The results are demonstrated using a low-speed, single stage, axial flow compressor.
peed, single stage, axial flow compressor.  +
• Aircraft operate in different modes during
Aircraft operate in different modes during flight, corresponding to different flight conditions and control schemes. We use differential flatness of an approximate model of the pitch dynamics of a thrust vectored aircraft to achieve fast switching between those modes. We investigate some methods to compensate for the perturbations to flatness. Simulations and experimental data are provided to validate the approach.
ata are provided to validate the approach.  +
• An experimental investigation of acoustic
An experimental investigation of acoustic mode noise suppression was conducted in a cavity using a digital controller with a linear control algorithm. The control algorithm was based on flow field physics similar to the Rossiter model for acoustic resonance. Details of the controller and results from its implementation are presented in the companion paper by Rowley, et al (2002). Here the experiments and some details of the flow field development are described, which were done primarily at Mach number 0.34 corresponding to single mode resonance in the cavity. A novel method using feedback control to suppress the resonant mode and open-loop forcing to inject a non-resonant mode was developed for system identification. The results were used to obtain empirical transfer functions of the components of resonance, and measurements of the shear layer growth for use in the design of the control algorithm.
se in the design of the control algorithm.  +
• An ongoing area of study in synthetic biol
An ongoing area of study in synthetic biology has been the design and construction of synthetic circuits that maintain homeostasis at the population level. Here, we are interested in designing a synthetic control circuit that regulates the total cell population and the relative ratio between cell strains in a culture containing two different cell strains. We have developed a dual feedback control strategy that uses two separate control loops to achieve the two functions respectively. By combining both of these control loops, we have created a population regulation circuit where both the total population size and relative cell type ratio can be set by reference signals. The dynamics of the regulation circuit show robustness and adaptation to perturbations in cell growth rate and changes in cell numbers. The control architecture is general and could apply to any organism for which synthetic biology tools for quorum sensing, comparison between outputs, and growth control are available.
outputs, and growth control are available.  +
• An outstanding challenge in the design of
An outstanding challenge in the design of synthetic biocircuits is the development of a robust and efficient strategy for interconnecting functional modules. Recent theoretical work demonstrated that a phosphorylation based insulator implementing a dual strategy of high gain and strong negative feedback could potentially serve as a device to attenuate retroactivity. This research investigates the structural identifiability of the phoshorylation based insulator when implemented in an {\it in vitro} transcription-translation cell free expression system. We consider a complex model that provides an intricate description of all chemical reactions and leveraging specific physiologically plausible assumptions, we derive a rigorous simplified model that captures the output dynamics of the phosphorylation based insulator. We perform standard system identification analysis and determine that the model is globally identifiable with respect to three critical parameters. Our findings show the utility of the transcription-translation cell free expression system as a platform for system identification, as it provides extra control inputs for parameter estimation that typically are unavailable in vivo. The parameters estimated are then used as a basis for a simulation study in a parallel experimental work (also submitted to qBio-2014).
mental work (also submitted to qBio-2014).  +
• Analysis and simulations are performed for
Analysis and simulations are performed for a simplified model of a commercially available variant on the skateboard, known as the Snakeboard. Although the model exhibits basic gait patterns seen in a large number of locomotion problems, the analysis tools currently available do not apply to this problem. The difficulty is seen to lie primarily in the way in which the nonholonomic constraints enter into the system. As a first step towards understanding systems represented by our model we present the equations of motion and perform some controllability analysis for the snakeboard. We also perform some numerical simulations of the gait patterns.
umerical simulations of the gait patterns.  +
• Application of synthetic biology is limite
Application of synthetic biology is limited by the capacity of cells to faithfully execute burdensome engineered functions in the face of Darwinian evolution. Division of labor, both metabolic and reproductive, are underutilized in confronting this barrier. To address this, we developed a serine-integrase based differentiation circuit that allows control of the population composition through tuning of the differentiation rate and number of cell divisions differentiated cells can undergo. We applied this system to T7 RNAP-driven expression of a fluorescent protein, and demonstrate both increased duration of circuit function and total production for high burden expression. While T7 expression systems are typically used for high-level short-term expression, this system enables longer duration production, and could be readily applied to burdensome or toxic products not readily produced in bacteria.
products not readily produced in bacteria.  +
• As a field, synthetic biology strives to e
As a field, synthetic biology strives to engineer increasingly complex artificial systems in living cells. Active feedback in closed loop systems offers a dynamic and adaptive way to ensure constant relative activity independent of intrinsic and extrinsic noise. In this work, we use synthetic protein scaffolds as a modular and tunable mechanism for concentration tracking through negative feedback. Input to the circuit initiates scaffold production, leading to colocalization of a two-component system and resulting in the production of an inhibitory antiscaffold protein. Using a combination of modeling and experimental work, we show that the biomolecular concentration tracker circuit achieves dynamic protein concentration tracking in ''Escherichia coli'' and that steady state outputs can be tuned.
nd that steady state outputs can be tuned.  +
• As a step towards achieving autonomy in sp
As a step towards achieving autonomy in space exploration missions we consider a collaborative robotics system with a copter and a rover. The goal of the copter is to explore an unknown environment so as to maximize knowledge about a science mission expressed in Linear Temporal Logic that is to be executed by the rover. We model environmental uncertainty as a belief space Markov Decision Process and formulate the problem as a two-step stochastic dynamic program that we solve in a way that leverages the decomposed nature of the overall system. We demonstrate in simulations that the robot team makes intelligent decisions in the face of uncertainty.
gent decisions in the face of uncertainty.  +
• As studies continue to demonstrate how our
As studies continue to demonstrate how our health is related to the status of our various commensal microbiomes, synthetic biologists are developing tools and approaches to control these microbiomes and stabilize healthy states or remediate unhealthy ones. Building on previous work to control bacterial communities, we have constructed a synthetic two-member bacterial consortium engineered to reach population density and composition steady states set by inducer inputs. We detail a screening strategy to search functional parameter space in this high-complexity genetic circuit as well as initial testing of a functional two-member circuit. We demonstrate non-independent changes in total population density and composition steady states with a limited set of varying inducer concentrations. After a dilution to perturb the system from its steady state, density and composition steady states are not regained. Modeling and simulation suggest a need for increased degradation of intercellular signals to improve circuit performance. Future experiments will implement increased signal degradation and investigate the robustness of control of each characteristic to perturbations from steady states.
istic to perturbations from steady states.  +
• Average consensus is a widely used algorit
Average consensus is a widely used algorithm for distributed averaging, where all the agents in the network constantly communicate and update their states in order to achieve an agreement. This approach could result in an undesirable disclosure of information on the initial state of agent i to other agents. In this paper, we propose a Privacy Preserving Average Consensus (PPAC) algorithm to guarantee the privacy of the initial state and the convergence to the exact initial values, by adding and subtracting random noises to the consensus process. We characterize the mean square convergence rate of the PPAC algorithm and derive upper and lower bounds for the covariance matrix of the maximum likelihood estimate on the initial state. We further provide an algebraic condition under which the PPAC algorithm is (epsilon, delta)-differentially private. A numerical example is provided to illustrate the effectiveness of the PPAC algorithm.
e the effectiveness of the PPAC algorithm.  +
• Bifurcations are ubiquitous in engineering
Bifurcations are ubiquitous in engineering applications. Subcritical bifurcations are typically associated with hysteresis and catastrophic instability inception, while supercritical bifurcations are usually associated with gradual and more benign instability inception. With the assumption that the bifurcating modes are linearly unstabilizable, we give a constructive procedure of designing feedback laws to change the criticality of bifurcations from subcritical to supercritical. Algebraic necessary and sufficient conditions are obtained under which the criticality of a simple steady-state or Hopf bifurcation can be changed to supercritical by a smooth feedback. The effects of magnitude saturation, bandwidth, and rate limits are important issues in control engineering. We give qualitative estimates of the region of attraction to the stabilized bifurcating equilibrium/periodic orbits under these constraints. <p> We apply the above theoretical results to the Moore-Greitzer model in active control of rotating stall and surge in gas turbine engines. Though linear stabilizability can be achieved using distributed actuation, it limits the practical usefulness due to considerations of affordability and reliability. On the other hand, simple but practically promising actuation schemes such as outlet bleed valves, a couple of air injectors, and magnetic bearings will make the system loss of linear stabilizability, thus the control design becomes a challenging task. The above mentioned theory in bifurcation stabilization can be applied to these cases. We analyze the effects of magnitude and rate saturations in active control of rotating stall using bleed valves. Analytic formulas are obtained for the operability enhancement as a function of system parameters, noise level, and actuator magnitude and rate limits. The formulas give good qualitative predictions when compared with experiments. Our conclusion is that actuator magnitude and rate limits are serious limiting factors in stall control and must be addressed in practical implementation to the aircraft engines. <p>
ntation to the aircraft engines. <p>  +
• Biological organisms use their sensory sys
Biological organisms use their sensory systems to detect changes in their environment. The ability of sensory systems to adapt to static inputs allows wide dynamic range as well as sensitivity to input changes including fold-change detection, a response that de- pends only on fold changes in input, and not on ab- solute changes. This input scale invariance underlies an important strategy for search that depends solely on the spatial profile of the input. Synthetic efforts to reproduce the architecture and response of cellu- lar circuits provide an important step to foster under- standing at the molecular level. We report the bottom- up assembly of biochemical systems that show exact adaptation and fold-change detection. Using a malachite green aptamer as the output, a synthetic tran- scriptional circuit with the connectivity of an incoherent feed-forward loop motif exhibits pulse generation and exact adaptation. A simple mathematical model was used to assess the amplitude and duration of pulse response as well as the parameter regimes required for fold-change detection. Upon parameter tuning, this synthetic circuit exhibits fold-change detection for four successive rounds of two-fold input changes. The experimental realization of fold-change detection circuit highlights the programmability of transcriptional switches and the ability to obtain predictive dynamical systems in a cell-free environment for technological applications.
nvironment for technological applications.  +
• Biological signaling systems not only dete
Biological signaling systems not only detect the absolute levels of the signals, but are also able to sense the fold-changes of the signals. The ability to detect fold-changes provides a powerful tool for biological organisms to adapt to the changes in environment. Here we present the first novel syn- thetic fold-change detector (FCD) circuit built from ground up in vivo. We systematically designed the FCD circuit in silico, prototyped it in cell-free transcription-translation platform (TX-TL), and eventually implemented it in E. coli cells. We were able to show that the FCD circuit can not only generate pulse-like behavior in response to input, but also produce the same pulse response with inputs of the same fold-change, despite of di�erent absolute signal levels.
espite of di�erent absolute signal levels.  +
• Biomolecular circuits with two distinct an
Biomolecular circuits with two distinct and stable steady states have been identified as essential components in a wide range of biological networks, with a variety of mechanisms and topologies giving rise to their important bistable property. Understanding the differences between circuit implementations is an important question, particularly for the synthetic biologist faced with determining which bistable circuit design out of many is best for their specific application. In this work we explore the applicability of Sturm's theorem—a tool from nineteenth-century real algebraic geometry—to comparing ‘functionally equivalent’ bistable circuits without the need for numerical simulation. We first consider two genetic toggle variants and two different positive feedback circuits, and show how specific topological properties present in each type of circuit can serve to increase the size of the regions of parameter space in which they function as switches. We then demonstrate that a single competitive monomeric activator added to a purely monomeric (and otherwise monostable) mutual repressor circuit is sufficient for bistability. Finally, we compare our approach with the Routh–Hurwitz method and derive consistent, yet more powerful, parametric conditions. The predictive power and ease of use of Sturm's theorem demonstrated in this work suggest that algebraic geometric techniques may be underused in biomolecular circuit analysis.
nderused in biomolecular circuit analysis.  +
• Borrowing a concept from hydrodynamic anal
Borrowing a concept from hydrodynamic analysis, this paper presents stream functions which satisfy Laplace's equation as a local-minima free method for producing potential-field based navigation functions in two dimensions. These functions generate smoother paths (i.e. more suited to aircraft-like vehicles) than previous methods. A method is developed for constructing analytic stream functions to produce arbitrary vehicle behaviors while avoiding obstacles, and an exact solution for the case of a single uniformly moving obstacle is presented. The effects of introducing multiple obstacles are discussed and current work in this direction is detailed. Experimental results generated on the Cornell RoboFlag testbed are presented and discussed.
oFlag testbed are presented and discussed.  +
• Caltech's ducted fan experiment is used as
Caltech's ducted fan experiment is used as a case study to investigate the properties of an algorithm for uniting local and global controllers proposed in (Teel and Kapoor, 1997) To simplify the control design process and to illustrate robustness, the ducted fan is modeled as a linear system with input rate limits. The local controller is an (fairly aggressive) LQR state feedback while the (semi-)global controller is a much less aggressive LQR state feedback. Closed-loop simulation results are provided using a fully nonlinear model of the ducted fan derived from wind tunnel data. Experimental results are also provided using the actual Caltech ducted fan.
vided using the actual Caltech ducted fan.  +
• Cells must detect and respond to molecular
Cells must detect and respond to molecular events such as the presence or absence of specific small molecules. To accomplish this, cells have evolved methods to measure the presence and concentration of these small molecules in their environment and enact changes in gene expression or behavior. However, cells don’t usually change their DNA in response to outside stimuli. In this work, we have engineered a genetic circuit that can enact specific and controlled genetic changes in response to small molecule stimuli. Known DNA sequences can be repeatedly integrated in a genomic array such that their identity and order encodes information about past small molecule concentrations that the cell has experienced. To accomplish this, we use catalytically inactive CRISPR-Cas9 (dCas9) to bind to and block attachment sites for the integrase Bxb1. Therefore, through the co-expression of dCas9 and guide RNA, Bxb1 can be directed to integrate one of two engineered plasmids, which correspond to two orthogonal small molecule inducers that can be recorded with this system. We identified the optimal location of guide RNA binding to the Bxb1 attP integrase attachment site, and characterized the detection limits of the system by measuring the minimal small molecule concentration and shortest induction time necessary to produce measurable differences in array composition as read out by Oxford Nanopore sequencing technology.
by Oxford Nanopore sequencing technology.  +
• Classification of stabilizability is obtai
Classification of stabilizability is obtained for multi-input nonlinear systems possessing a simple steady-state or Hopf bifurcation with the critical mode being linearly uncontrollable. Stabilizability is defined as the existence of a sufficiently smooth state feedback such that the bifurcation for the closed loop system is supercritical, and in the meantime, the linearly controllable modes are locally asymptotically stable. Necessary and sufficient conditions of stabilizability are derived under certain nondegeneracy conditions. Explicit construction of stabilizing feedbacks is obtained for the cases when the system is stabilizable.
the cases when the system is stabilizable.  +
• Consensus protocols in coordinated multi-a
Consensus protocols in coordinated multi-agent systems are distributed algorithms. Just using local information available to each single agent, all agents converge to an identical consensus state and the convergence speed is determined by the algebraic connectivity of the communication network. In order to achieve a faster consensus seeking, we propose multi-hop relay protocols based on the current nearest neighbor rules'' consensus protocols. By employing multiple-hop paths in the network, more information is passed around and each agent enlarges its "available" neighborhood. We demonstrate that these relay protocols can increase the algebraic connectivity without physically adding or changing any communication links. Moreover, time delay sensitivity of relay protocols are discussed in detail. We point out that a trade off exists between convergence performance and time delay robustness. Simulation results are also provided to verify the efficiency of relay protocols.
verify the efficiency of relay protocols.  +
• Control of vehicle formations has emerged
Control of vehicle formations has emerged as a topic of significant interest to the controls community. In this paper, we merge tools from graph theory and control theory to derive stability criteria for formation stabilization. The interconnection between vehicles (i.e., which vehicles are sensed by other vehicles) is modeled as a graph, and the eigenvalues of the Laplacian matrix of the graph are used in stating a Nyquist-like stability criterion for vehicle formations. The location of the Laplacian eigenvalues can be correlated to the graph structure, and therefore used to identify desirable and undesirable formation interconnection topologies.
able formation interconnection topologies.  +
• Control of vehicle formations has emerged
Control of vehicle formations has emerged as a topic of significant interest to the controls community. In applications such as microsatellites and underwater vehicles, formations have the potential for greater functionality and versatility than individual vehicles. In this thesis, we investigate two topics relevant to control of vehicle formations: optimal vehicle control and cooperative control.
ehicle control and cooperative control.  +
• Controllers developed for control of flexi
Controllers developed for control of flexible-link robots in hybrid force-position control tasks by a new singular perturbation analysis of flexible manipulators are implemented on an experimental two-robot grasping setup. Various performance criteria are set up and experimental results are discussed within that setting to show tradeoffs in using flexible link robots for grasping. We conclude that large flexibility can be controlled without too much additional effort, has performance comparable to rigid robots and possesses enhancing properties which make it attractive for use in certain types of applications.
for use in certain types of applications.  +
• Conventional simultaneous localization and
Conventional simultaneous localization and map- ping (SLAM) algorithms rely on geometric measurements and require loop-closure detections to correct for drift accumulated over a vehicle trajectory. Semantic measurements can add measurement redundancy and an alternative form of loop closure. We propose two different estimation algorithms that incorporate semantic measurements provided by vision-based object classifiers. An a priori map of regions where the objects can be detected is assumed. The first estimation framework is posed as a maximum-likelihood problem, where the likelihood function for semantic measurements is derived from the con- fusion matrices of the object classifiers. The second estimation framework is comprised of two parts: 1) a continuous-state estimation formulation that includes semantic measurements as a form of state constraints and 2) a discrete-state estimation formulation used to compute the certainty of object detection measurements using a Hidden Markov Model (HMM). The advantages of incorporating semantic measurements in these frameworks are demonstrated in numerical simulations. In particular, the proposed estimation algorithms improve upon the robustness and accuracy of conventional SLAM algorithms. Also, the certainty metric of object detection measurements derived from the HMM in our simulation are greater than the certainty levels provided by the confusion matrix in object classification algorithms.
atrix in object classification algorithms.  +
• Convergence properties of distributed cons
Convergence properties of distributed consensus protocols on networks of dynamical agents have been analyzed by combinations of algebraic graph theory and control theory tools under certain assumptions, such as strong connectivity. Strong connectivity can be regarded as the requirement that the information of each agent propagates to all the others, possibly with intermediate steps and manipulations. However, because of network failures or malicious attacks, it is possible that this assumption no longer holds, so that some agents are only receiving or only transmitting information from other subsets of agents. In this case, strong connectivity is replaced by weak connectivity. We analyze the convergence properties of distributed consensus on directed graphs with weakly connected components. We show conditions for which the agreement is reached, and, for the cases in which such conditions do not hold, we provide bounds on the residual disagreement. in terms of the number of agents that must fail for the
he number of agents that must fail for the  +
• Correct-by-construction synthesis of high-
Correct-by-construction synthesis of high-level re- active control relies on the use of formal methods to generate controllers with provable guarantees on their behavior. While this approach has been successfully applied to a wide range of systems and environments, it scales poorly with the increasing size of the environment. A receding horizon framework was recently proposed to mitigate this computational blowup, by decomposing the global control problem into several tractable subproblems. The existence of a global controller is ensured through symbolic checks of the specification, and local controllers are synthesized when needed, using the current state of the environment as the initial condition. This reduces the size of the synthesized strategy, but does not provide much improvement for problems with large dynamic environments, because the large number of possible global environment strategies. Ad hoc methods to locally restrict the environment have previously been used, at the risk of losing correctness. This paper presents a method of reducing specifications by eliminating locally redundant variables, while maintaining the correctness of controllers. We demonstrate the method using an autonomous car example, on problem sizes that were previously unsolvable due to the number of variables in the environment. We also demonstrate how the reduced specifications can be used to identify opportunities for reusing the synthesized local controllers.
reusing the synthesized local controllers.  +
• Crosstalk is defined as the set of unwante
Crosstalk is defined as the set of unwanted interactions among the different entities of a network. Crosstalk is present in various degrees in every system where information is transmitted through a means that is accessible by all the individual units of the network. Using concepts from graph theory, we introduce a quantifiable measure for sensitivity to crosstalk, and analytically derive the structure of the networks in which it is minimized. It is shown that networks with an inhomogeneous degree distribution are more robust to crosstalk than corresponding homogeneous networks. We provide a method to construct the graph with the minimum possible sensitivity to crosstalk, given its order and size. Finally, for networks with a fixed degree sequence, we present an algorithm to find the optimal interconnection structure among their vertices.
connection structure among their vertices.  +