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• Experimental Demonstration of the Dynamics and Stability of a Low Reynolds Number Swimmer Near a Plane Wall  + (The motion of microorganisms as well as of … The motion of microorganisms as well as of tiny robotic swimmers for biomedical applications is governed by low Reynolds number (Re) hydrodynamics, where viscous effects dominate and inertial effects are negligible. This paper presents experimental results that verify theoretical predictions of our recent work which analyzed the dynamics and stability of a low-Re swimmer near a plane wall. The experimental setup uses macro-scale swimmer prototypes which are propelled by rotating cylinders in highly viscous silicone oil. The motion was recorded by a video camera and position measurements were taken by an optical tracking system. The results show good qualitative agreement with our recent theoretical predictions.t with our recent theoretical predictions.)
• Simple Delay-Based Implementation of Continuous-Time Controllers  + (The objective of this work is to study the … The objective of this work is to study the benefits that delay can provide in simplifying the control process of large-scale systems, motivated by the availability of different types of delays in man-made and biological systems. We show that a continuous-time linear time-invariant (LTI) controller can be approximated by a simple controller that mainly uses delay blocks instead of integrators. More specifically, three methods are proposed to approximate a pre-designed stabilizing LTI controller arbitrarily precisely by a simple delay-based controller composed of delay blocks, a few integrators and possibly a unity feedback. Different problems associated with the developed approximation procedures, such as finding the optimal number of delay blocks or studying the robustness of the designed controller with respect to delay values, are then addressed.spect to delay values, are then addressed.)
• Observability of a Class of Hybrid Systems on Bounded Lattices  + (The observability properties of a class of … The observability properties of a class of hybrid</br>systems whose continuous variables are available for measurement</br>are considered. We show that the discrete variables'</br>dynamics can be always extended for observable systems to</br>a lattice in such a way that the extended system has the</br>properties that allow the construction of the LU discrete</br>state estimator. Such an estimator updates two variables at</br>each step, namely the upper and lower bound of the set</br>of all possible discrete variables' values compatible with the</br>output sequence. We give an estimate of the complexity of the</br>estimator in the worst case.lexity of the estimator in the worst case.)
• Implementation And Simulation Of Phosphorylation-Based Insulator In Transcription-Translation Platform  + (The operational amplifier (OPAMP) is a ver … The operational amplifier (OPAMP) is a very useful insulation module in electric circuits to avoid loading effect (retroactivity). In synthetic biological circuits, we also have the same retroactivity problem, in which the biomolecular systems are not always modular due to downstream components. The output of the upstream component will be affected as the downstream component sequesters that output, which in turn impedes the process of constructing more complex biocircuits. To address this obstacle, the retroactivity needs to be attenuated by implementing a similar OPAMP device using biocircuits. Previous theoretical papers suggested a potential function of a phosphorylation based circuit in providing the feature of atten- uating retroactivity. Here we presented a successful prototyping and implementation of such a phosphorylation-based insulator (PBI) in an in vitro cell-free transcription-translation system (TX- TL). We demonstrated that retroactivity also exists in TX-TL system, if not stronger, by testing a simple negative regulation circuit. Besides we showed that the TX-TL system contains all the protein, DNA components and other resources required for the PBI circuit to work properly. We then demonstrated that the PBI circuit helps minimizing the loading effect to less than 10% compared to control circuit. With this preliminary PBI circuit design, attenuation of retroactivity while connecting two modules in vitro becomes possible. In concert with another paper from our group (E. Yeung, S. Guo, R. Murray QBIO2014) which used system identification to estimate all three essential parameters in a simplified PBI model, we showed that the simulations based on these parameters match the experimental data very well and provide an interesting insight into future designs.n interesting insight into future designs.)
• Geometric trajectory filtering via numerical conformal mapping  + (The paper studies the problem which we ref … The paper studies the problem which we refer to as geometric trajectory filtering, where only trajectories that satisfy the local safety constraints are selected from a library of trajectories. The goal is to speed up primitive-based motion planning while still maintaining a relatively a large collection of motion primitives. One way to solve this problem is to obtain a proper (preferably smooth) function, referred to as the containment indicator function, that describes the shape of the free space. To construct the containment indicator function for an arbitrary shape, the paper uses conformal mapping to transform the original shape of interest to a simpler target shape (e.g. disk, rectangle), which can then be characterized by elementary functions. Computational methods for finding the desired conformal maps are studied. It is shown that they can be formulated as convex optimization problems, whose solution can be obtained efficiently.hose solution can be obtained efficiently.)
• Learning diffeomorphism models of robotic sensorimotor cascades  + (The problem of bootstrapping consists in d … The problem of bootstrapping consists in designing agents that can learn from scratch the model of their sensori- motor cascade (the series of robot actuators, the external world, and the robot sensors) and use it to achieve useful tasks. In principle, we would want to design agents that can work for any robot dynamics and any robot sensor(s). One of the difficulties of this problem is the fact that the observations are very high dimensional, the dynamics is nonlinear, and there is a wide range of "representation nuisances" to which we would want the agent to be robust. In this paper, we model the dynamics of sensorimotor cascades using diffeomorphisms of the sensel space. We show that this model captures the dynamics of camera and range-finder data, that it can be used for long-term predictions, and that it can capture nonlinear phenomena such as a limited field of view. Moreover, by analyzing the learned diffeomorphisms it is possible to recover the "linear structure" of the dynamics in a manner which is independent of the commands representation.ndependent of the commands representation.)
• Discrete State Estimators for a Class of Nondeterministic Hybrid Systems on a Lattice  + (The problem of estimating the discrete var … The problem of estimating the discrete variables</br>in nondeterministic hybrid systems where the continuous</br>variables are available for measurement is considered. Using</br>partial order and lattice theory, we construct a discrete state</br>estimator, the LU estimator, which updates two variables at</br>each step. Namely, it updates the lower (L) and upper (U)</br>bounds of the set of all possible discrete variables values</br>compatible with the output sequence and with the systems'</br>dynamics. If the system is weakly observable, we show that</br>there always exist a lattice on which to construct the LU</br>estimator. For computational issues, some partial orders are to</br>be preferred to others.We thus show that nondeterminism may</br>be added to a system so as to obtain a new system that satisfies</br>the requirements for the construction of the LU estimator on</br>a chosen lattice. These ideas are applied to a nondeterministic</br>multi-robot system. to a nondeterministic multi-robot system.)
• Nonlinear Trajectory Generation for Unmanned Air Vehicles with Multiple Radars  + (The problem of finding a real time optimal … The problem of finding a real time optimal</br>trajectory to minimize the probability of detection (to maximize</br>the probability of notbeingdetected, pnd, function) of</br>unmanned air vehicles by opponent radar detection systems</br>is investigated. This paper extends our preliminary results</br>on low observable trajectory generation in three ways. First,</br>trajectory planning in the presence of detection by multiple</br>radar systems, rather than single radar systems, is considered.</br>Second, an overall probability of detection function is</br>developed for the multiple radar case. In previous work, both</br>probability of detection by a single radar and signature were</br>developed in the theory section, but the examples used only</br>signature constraints. In this work, the use of the overall</br>probability of detection function is used, both because it</br>aids in the extension to multiple radar systems and because</br>it is a more direct measure of the desirable optimization</br>criteria. The third extension is the use of updated signature</br>and probability of detection models. The new models have a</br>greater number of sharp gradients than the previous models,</br>with low detectability regions for both a cone shaped areas</br>centered around the nose as in the previous paper, as well as a</br>cone-shaped area centered around rear of the air vehicle. The</br>Nonlinear Trajectory Generation method (NTG), developed</br>at Caltech, is used and motivated by the ability to provide</br>real time solutions for constrained nonlinear optimization</br>problems. Numerical simulations of multiple radar scenarios</br>illustrate UAV trajectories optimized for both detectability and</br>time.optimized for both detectability and time.)
• Model reduction of interconnected linear systems  + (The problem of model reduction of linear s … The problem of model reduction of linear systems with certain interconnection structure is considered </br>in this paper. To preserve the interconnection structure between subsystems in the reduction, special </br>care needs to be taken. This problem is important and timely because of the recent focus on complex </br>networked systems in control engineering. Two different model-reduction methods are introduced and </br>compared in the paper. Both methods are extensions to the well-known balanced truncation method. </br>Compared to earlier work in the area these methods use a more general linear fractional transformation </br>framework, and utilize linear matrix inequalities. Furthermore, new approximation error bounds that </br>reduce to classical bounds in special cases are derived. So-called structured Hankel singular valueso-called structured Hankel singular values)
• Formal Test Synthesis for Safety-Critical Autonomous Systems based on Control Barrier Functions  + (The prolific rise in autonomous systems ha … The prolific rise in autonomous systems has led to questions regarding their safe instantiation in real-world scenarios. Failures in safety-critical contexts such as human-robot interactions or even autonomous driving can ultimately lead to loss of life. In this context, this paper aims to provide a method by which one can algorithmically test and evaluate an autonomous system. Given a black-box autonomous system with some operational specifications, we construct a minimax problem based on control barrier functions to generate a family of test parameters designed to optimally evaluate whether the system can satisfy the specifications. To illustrate our results, we utilize the Robotarium as a case study for an autonomous system that claims to satisfy waypoint navigation and obstacle avoidance simultaneously. We demonstrate that the proposed test synthesis framework systematically finds those sequences of events (tests) that identify points of system failure.s) that identify points of system failure.)
• Engineering Transcriptional Regulator Effector Specificity Using Computational Design and In Vitro Rapid Prototyping: Developing a Vanillin Sensor  + (The pursuit of circuits and metabolic path … The pursuit of circuits and metabolic pathways of increasing complexity and robustness in synthetic biology will require engineering new regulatory tools. Feedback control based on relevant molecules, including toxic intermediates and environmental signals, would enable genetic circuits to react appropriately to changing conditions. In this work, variants of qacR, a tetR family repressor, were generated by computational protein design and screened in a cell-free transcription-translation (TX-TL) system for responsiveness to a new targeted effector. The modified repressors target vanillin, a growth-inhibiting small molecule found in lignocellulosic hydrolysates and other industrial processes. Promising candidates from the in vitro screen were further characterized in vitro and in vivo in a gene circuit. The screen yielded two qacR mutants that respond to vanillin both in vitro and in vivo. While the mutants exhibit some toxicity to cells, presumably due to off-target effects, they are prime starting points for directed evolution toward vanillin sensors with the specifications required for use in a dynamic control loop. We believe this process, a combination of the generation of variants coupled with in vitro screening, can serve as a framework for designing new sensors for other target compounds.ng new sensors for other target compounds.)
• Engineering Transcriptional Regulator Effector Specificity using Computational Design and In Vitro Rapid Prototyping: Developing a Vanillin Sensor  + (The pursuit of circuits and metabolic path … The pursuit of circuits and metabolic pathways of increasing complexity and robustness in synthetic biology will require engineering new regulatory tools. Feedback control based on relevant molecules, including toxic intermediates and environmental signals, would enable genetic circuits to react appropriately to changing conditions. In this work, variants of qacR, a tetR family repressor, were generated by compu- tational protein design and screened in a cell-free transcription-translation (TX-TL) system for responsiveness to a new targeted effector. The modified repressors target vanillin, a growth-inhibiting small molecule found in lignocellulosic hydrolysates and other industrial processes. Promising candidates from the in vitro screen were further characterized in vitro and in vivo in a gene circuit. The screen yielded two qacR mutants that respond to vanillin both in vitro and in vivo. We believe this process, a combination of the generation of variants coupled with in vitro screening, can serve as a framework for designing new sensors for other target compounds.ng new sensors for other target compounds.)
• Engineering Transcriptional Regulator Effector Specificity Through Rational Design and Rapid Prototyping  + (The pursuit of circuits and metabolic path … The pursuit of circuits and metabolic pathways of increasing complexity and robustness in synthetic biology will require engineering new regulatory tools. Feedback control based on relevant molecules, including toxic intermediates and environmental signals, would enable genetic circuits to react appropriately to changing conditions. In this work, computational protein design was used to create functional variants of qacR, a tetR family repressor, responsive to a new targeted effector. The modified repressors target vanillin, a growth-inhibiting small molecule found in lignocellulosic hydrolysates and other industrial processes. A computatio ally designed library was screened using an in vitro transcription-translation (TX-TL) system. Leads from the in vitro screen were characterized in vivo. Preliminary results demonstrate dose-dependent regulation of a downstream fluorescent reporter by vanillin. These repressor designs provide a starting point for the evolution of improved variants. We believe this process can serve as a framework for designing new sensors for other target compounds.ng new sensors for other target compounds.)
• Timing molecular motion and production with a synthetic transcriptional clock  + (The realization of artificial biochemical … The realization of artificial biochemical reaction networks with unique functionality is one of the main challenges for the development of synthetic biology. Due to the reduced number of components, biochemical circuits constructed in vitro promise to be more amenable to systematic design and quantitative assessment than circuits embedded within living organisms. To make good on that promise, effective methods for composing subsystems into larger systems are needed. Here we used an artificial biochemical oscillator based on in vitro transcription and RNA degradation reactions to drive a variety of âloadâ processes such as the operation of a DNA-based nanomechanical device (âDNA tweezersâ) or the production of a functional RNA molecule (an aptamer for malachite green). We implemented several mechanisms for coupling the load processes to the oscillator circuit and compared them based on how much the load affected the frequency and amplitude of the core oscillator, and how much of the load was effectively driven. Based on heuristic insights and computational modeling, an âinsulator circuitâ was developed, which strongly reduced the detrimental influence of the load on the oscillator circuit. Understanding how to design effective insulation between biochemical subsystems will be critical for the synthesis of larger and more complex systems.thesis of larger and more complex systems.)
• Quantitative Modeling of Integrase Dynamics Using a Novel Python Toolbox for Parameter Inference in Synthetic Biology  + (The recent abundance of high-throughput da … The recent abundance of high-throughput data for biological circuits enables data-driven quantitative modeling and parameter estimation. Common modeling issues include long computational times during parameter estimation, and the need for many iterations of this cycle to match data. Here, we present BioSCRAPE (Bio-circuit Stochastic Single-cell Reaction Analysis and Parameter Estimation) - a Python package for fast and flexible modeling and simulation for biological circuits. The BioSCRAPE package can be used for deterministic or stochastic simulations and can incorporate delayed reactions, cell growth, and cell division. Simulation run times obtained with the package are comparable to those obtained using C code - this is particularly advantageous for computationally expensive applications such as Bayesian inference or simulation of cell lineages. We first show the package's simulation capabilities on a variety of example simulations of stochastic gene expression. We then further demonstrate the package by using it to do parameter inference for a model of integrase dynamics using experimental data. The BioSCRAPE package is publicly available online along with more detailed documentation and examples. more detailed documentation and examples.)
• Identification of Decision Rules in a Human-controlled System: Vehicles at a Traffic Intersection  + (The rules that govern decision making in s … The rules that govern decision making in systems</br>controlled by humans are often simple to describe. However,</br>deriving these rules from the actions of a group can be very</br>difficult, making human behavior hard to predict. We develop</br>an algorithm to determine the rules implemented by drivers</br>at a traffic intersection by observing the trajectories of their</br>cars. We applied such algorithm to a traffic intersection scenario</br>reproduced in the Caltech multi-vehicle lab, with human subjects</br>remotely driving kinematic robots. The results obtained on these</br>data suggest that this kind of human behavior is to some extent</br>predictable on our data set, and different subjects implement</br>similar rules.ifferent subjects implement similar rules.)
• Nonlinear Control of Rotating Stall and Surge with Axisymmetric Bleed and Air Injection on Axial Flow Compressors  + (The study of compressor instabilities in g … The study of compressor instabilities in gas turbine engines has received</br>much attention in recent years. In particular, rotating stall and surge</br>are major causes of problems ranging from component stress and lifespan</br>reduction to engine explosion. In this thesis, modeling and control of</br>rotating stall and surge using bleed valve and air injection is studied and</br>validated on a low speed, single stage, axial compressor at Caltech.</br><p></br>Bleed valve control of stall is achieved only when the compressor</br>characteristic is actuated, due to the fast growth rate of the stall cell</br>compared to the rate limit of the valve. Furthermore, experimental results</br>show that the actuator rate requirement for stall control is reduced by a</br>factor of fourteen via compressor characteristic actuation. Analytical</br>expressions based on low order models (2--3 states) and a high fidelity</br>simulation (37 states) tool are developed to estimate the minimum rate</br>requirement of a bleed valve for control of stall. A comparison of the</br>tools to experiments show a good qualitative agreement, with increasing</br>quantitative accuracy as the complexity of the underlying model increases.</br><p></br>Air injection control of stall and surge is also investigated.</br>Simultaneous control of stall and surge is achieved using axisymmetric air</br>injection. Three cases with different injector back pressure are studied.</br>Surge control via binary air injection is achieved in all three cases.</br>Simultaneous stall and surge control is achieved for two of the cases, but</br>is not achieved for the lowest authority case. This is consistent with</br>previous results for control of stall with axisymmetric air injection</br>without a plenum attached.</br><p></br>Non--axisymmetric air injection control of stall and surge is also studied.</br>Three existing control algorithms found in literature are modeled and</br>analyzed. A three--state model is obtained for each algorithm. For two</br>cases, conditions for linear stability and bifurcation criticality on</br>control of rotating stall are derived and expressed in terms of</br>implementation--oriented variables such as number of injectors. For the</br>third case, bifurcation criticality conditions are not obtained due to</br>complexity, though linear stability property is derived. A theoretical</br>comparison between the three algorithms is made, via the use of low--order</br>models, to investigate pros and cons of the algorithms in the context of</br>operability.</br><p></br>The effects of static distortion on the compressor facility at Caltech is</br>characterized experimentally. Results consistent with literature are</br>obtained. Simulations via a high fidelity model (34 states) are also</br>performed and show good qualitative as well as quantitative agreement to</br>experiments. A non--axisymmetric pulsed air injection controller for stall</br>is shown to be robust to static distortion.n controller for stall is shown to be robust to static distortion.)
• Temporal Logic Control of POMDPs via Label-based Stochastic Simulation Relations  + (The synthesis of controllers guaranteeing … The synthesis of controllers guaranteeing linear temporal logic specifications on partially observable Markov decision processes (POMDP) via their belief models causes computational issues due to the continuous spaces. In this work, we construct a finite-state abstraction on which a control policy is synthesized and refined back to the original belief model. We introduce a new notion of label- based approximate stochastic simulation to quantify the deviation between belief models. We develop a robust synthesis methodology that yields a lower bound on the satisfaction probability, by compensating for deviations a priori, and that utilizes a less conservative control refinement.es a less conservative control refinement.)
• Real-time trajectory generation for constrained nonlinear dynamical systems using non-uniform rational B-spline basis functions  + (The thesis describes a new method for obta … The thesis describes a new method for obtaining minimizers for optimal control problems whose minima serve as control policies for guiding nonlinear dynamical systems to achieve prescribed goals under imposed trajectory and actuator constraints. One of the major contributions of the present work resides in the approximation of such minimizers by piecewise polynomial functions expressed in terms of a linear combination of non-uniform rational B-spline (NURBS) basis functions and the judicious exploitation of the properties of the resulting NURBS curves to improve the computational effort often associated with solving optimal control problems for constrained dynamical systems. In particular, by exploiting the two structures combined in a NURBS curve, NURBS basis functions and an associated union of overlapping polytopes constructed from the coefficients of the linear combination, we are able to separate an optimal control problem into two subproblemstimal control problem into two subproblems)
• Counter-example Guided Learning of Bounds on Environment Behavior  + (There is a growing interest in building au … There is a growing interest in building autonomous systems that interact with complex environments. The difficulty associated with obtaining an accurate model for such environments poses a challenge to the task of assessing and guaranteeing the system’s performance. We present a data-driven solution that allows for a system to be evaluated for specification conformance without an accurate model of the environment. Our approach involves learning a conservative reactive bound of the environment’s behavior using data and specification of the system’s desired behavior. First, the approach begins by learning a conservative reactive bound on the environment’s actions that captures its possible behaviors with high probability. This bound is then used to assist verification, and if the verification fails under this bound, the algorithm returns counter-examples to show how failure occurs and then uses these to refine the bound. We demonstrate the applicability of the approach through two case-studies: i) verifying controllers for a toy multi-robot system, and ii) verifying an instance of human-robot interaction during a lane-change maneuver given real-world human driving data.euver given real-world human driving data.)
• Modeling and Control of Epitaxial Thin Film Growth  + (Thin film deposition is a manufacturing pro … Thin film deposition is a manufacturing process in which tolerances may approach</br>the size of individual atoms. The final film is highly sensitive to the processing</br>conditions, which can be intentionally manipulated to control film properties. A</br>lattice model of surface evolution during thin film growth captures many important</br>features, including the nucleation and growth of clusters of atoms and the</br>propagation of atomic-height steps. The dimension of this probabilistic master</br>equation is too large to directly simulate for any physically realistic domain, and</br>instead stochastic realizations of the lattice model are obtained with kinetic Monte</br>Carlo simulations.</br><p></br>In this thesis simpler representations of the master equation are developed for</br>use in analysis and control. The static map between macroscopic process conditions</br>and microscopic transition rates is first analyzed. In the limit of fast periodic</br>process parameters, the surface responds only to the mean transition rates, and,</br>since the map between process parameters and transition rates is nonlinear, new</br>effective combinations of transition rates may be generated. These effective rates</br>are the convex hull of the set of instantaneous rates.</br><p></br>The map between transition rates and expected film properties is also studied.</br>The dimension of a master equation can be reduced by eliminating or grouping</br>configurations, yielding a reduced-order master equation that approximates the</br>original one. A linear method for identifying the coefficients in a master equation</br>is then developed, using only simulation data. These concepts are extended to</br>generate low-order master equations that approximate the dynamic behavior seen</br>in large Monte Carlo simulations. The models are then used to compute optimal</br>time-varying process parameters.</br><p></br>The thesis concludes with an experimental and modeling study of germanium</br>film growth, using molecular beam epitaxy and reflection high-energy electron</br>diffraction. Growth under continuous and pulsed flux is compared in experiment,</br>and physical parameters for the lattice model are extracted. The pulsing accessible</br>in the experiment does not trigger a change in growth mode, which is consistent</br>with the Monte Carlo simulations. The simulations are then used to suggest other</br>growth strategies to produce rougher or smoother surfaces.ce rougher or smoother surfaces.)
• Reduction Strategies for Kinetic Monte Carlo Models of Thin Film Growth  + (Thin film deposition encompasses a variety … Thin film deposition encompasses a variety of physical processes,</br>which occur over a wide range of length and time scales. A major challenge in modeling and simulating thin film deposition is this disparity</br>in scales. In this study we focus on an atomic-scale lattice model of</br>surface processes. Kinetic Monte Carlo simulations provide stochastic</br>realizations of the surface evolution, which may then inform a reacting flow or heat transfer model. Unfortunately, these simulations are</br>extremely computationally intensive, particularly for design and optimization studies in which many cases are considered.</br><p></br>We develop reduced-order models of thin film growth using two techniques: balanced truncation and eigensystem realization. After identifying the underlying structure of the lattice model as a linear differential</br>equation, we apply the reduction techniques to obtain reduced-order</br>models of root-mean-square roughness and step edge density. Three</br>modes are needed for a very small model system, while only five modes</br>capture the evolution of a 200x200-site system over a range of growth</br>modes, from stochastic roughening to island nucleation and coalescence.roughening to island nucleation and coalescence.)
• Effective Transition Rates for Epitaxial Growth Using Fast Modulation  + (Thin film deposition is an industrially-im … Thin film deposition is an industrially-important process that is highly dependent on the process</br>conditions. Most films are grown under constant conditions, but a few studies show that modified</br>properties may be obtained with periodic inputs. However, assessing the effects of modulation</br>experimentally becomes impractical with increasing material complexity. Here we consider periodic</br>conditions in which the period is short relative to the time-scales of growth. We analyze a stochastic</br>model of thin film growth, computing effective transition rates associated with rapid periodic</br>process parameters. Combinations of effective rates may exist which are not attainable under</br>steady conditions, potentially enabling new film properties. An algorithm is presented to construct</br>the periodic input for a desired set of effective transition rates. These ideas are first illustrated</br>by two simple examples using kinetic Monte Carlo simulations and are then compared to existing</br>deposition techniques.ompared to existing deposition techniques.)
• Modeling and Control of Thin Film Morphology Using Unsteady Processing Parameters: Problem Formulation and Initial Results  + (Thin film deposition is an industrially-im … Thin film deposition is an industrially-important process to which control theory has not historically been applied. The need for control is growing as the size of integrated</br>circuits shrinks, requiring increasingly tighter tolerances in the manufacture of thin films. Our contributions in this study are two-fold: we formulate a model of thin film</br>growth as a control system and we examine the effects of fast periodic forcing.</br><p></br>We choose a lattice formulation of crystal growth as our physical model, which captures atomic length scale effects at a time scale compatible with film growth. We focus on the control of film morphology, or surface height profile. Although the system</br>dimension is high, the structure is simple: the dynamics and the output are linear in the state. We consider the process conditions as inputs, which alter the transition rate</br>functions. In the evolution equation, each of these nonlinear functions is multiplied by a linear vector field, yielding a system with a structure similar to a bilinear system.</br><p></br>The process conditions in some deposition methods are inherently unsteady, which</br>produces films with altered morphology. We use the model developed in this study to analyze the effects of fast periodic forcing on thin film evolution. With the method of</br>averaging we develop new effective transition rates which may produce film properties</br>unattainable with constant inputs. We show that these effective rates are the convex</br>hull of the set of rates associated with constant inputs. We present conditions on</br>the convex hull for which the finite-time and infinite-time reachability sets cannot be</br>expanded with fast periodic forcing. An example in which this forcing increases the</br>reachability set and produces more desirable morphology is also presented. produces more desirable morphology is also presented.)
• Fault-Tolerant Controller Design with Applications in Power Systems and Synthetic Biology  + (This paper deals with fault-tolerant contr … This paper deals with fault-tolerant controller design for linear time-invariant (LTI) systems with multiple actuators. Given some critical subsets of the actuators, it is assumed that every combination of actuators can fail as long as the set of the remaining actuators includes one of these subsets. Motivated by electric power systems and biological systems, the goal is to design a controller so that the closed-loop system satisfies two properties: (i) stability under all permissible sets of faults and (ii) better performance after clearing every subset of the existing faults in the system. It is shown that a state-feedback controller satisfying these properties exists if and only if a linear matrix inequality (LMI) problem is feasible. This LMI condition is then transformed into an optimal-control condition, which has a useful interpretation. The results are also generalized to output-feedback and decentralized control cases. The efficacy of this work is demonstrated by designing fault-tolerant speed governors for a power system. The results developed here can be extended to more general types of faults, where each fault can possibly affect all state-space matrices of the system.ct all state-space matrices of the system.)

• Control education for societal-scale challenges: A community roadmap  + (This article focuses on extending, dissemi … This article focuses on extending, disseminating and interpreting the findings of an IEEE Control Systems Society working group looking at the role of control theory and engineering in solving some of the many current and future societal challenges. The findings are interpreted in a manner designed to give focus and direction to both future education and research work in the general control theory and engineering arena, interpreted in the broadest sense. The paper is intended to promote discussion in the community and also provide a useful starting point for colleagues wishing to re-imagine the design and delivery of control-related topics in our education systems, especially at the tertiary level and beyond.pecially at the tertiary level and beyond.)
• Synthesis of Control Protocols for Autonomous Systems  + (This article provides a review of control … This article provides a review of control protocol synthesis techniques that incorporate methodologies from formal methods and control theory to provide correctness guarantee for different types of autonomous systems, including those with discrete and continuous state space. The correctness of the system is defined with respect to a given specification expressed as a formula in linear temporal logic to precisely describe the desired properties of the system. The formalism presented in this article admits non-determinism, allowing uncertainties in the system to be captured. A particular emphasis is on alleviating some of the difficulties, e.g., heterogeneity in the underlying dynamics and computational complexity, that naturally arise in the construction of control protocols for autonomous systems. control protocols for autonomous systems.)
• Robotic Control and Nonholonomic Motion Planning  + (This dissertation addresses the problem of … This dissertation addresses the problem of control and kinematic</br>planning for constrained robot systems. An example of a system of</br>this type is a multifingered robot hand grasping an object. The</br>individual fingers act as robot manipulators and are constrained by</br>their contact with the object. If the contacts allow rolling between</br>the object and the fingertips, it is possible for the constraints to</br>be nonholonomic. That is, the constraints may not restrict the</br>reachable configurations of the system, but rather, constrain only the</br>allowable velocities of the system.</br><p></br>Using the multifingered hand as a motivating example, this</br>dissertation presents a detailed analysis of the kinematics, dynamics,</br>and control of robot systems with contact constraints. In particular,</br>it presents a unified derivation of the dynamics of robot manipulators</br>with Pfaffian velocity constraints, including the nonholonomic case.</br>This derivation allows control laws to be specified which are provably</br>stable for an entire class of systems, including unconstrained robots,</br>robot hands, and other systems of multiple robots performing a</br>coordinated task. A method for building complex controllers which</br>respects this class of constraints is also developed using a set of</br>simple primitives which allow hierarchical control structures to be</br>created in an organized fashion.</br><p></br>Finally, the nonholonomic motion planning problem is introduced and</br>discussed in detail. Using tools from differential geometric control</br>theory, it is possible to classify and analyze systems with</br>nonholonomic constraints. A brief review of the necessary tools along</br>with a review of the current literature is presented. A practical</br>method for steering nonholonomic systems using sinusoids is derived</br>and applied to several kinematic systems with contact constraints.to several kinematic systems with contact constraints.)
• Exponential Stabilization of Driftless Nonlinear Control Systems  + (This dissertation lays the foundation for … This dissertation lays the foundation for practical exponential</br>stabilization of driftless control systems. Driftless systems have</br>the form $$\dot x = X_1(x)u_1+\cdots +X_m(x)u_m, \quad x\in\real^n$$.</br>Such systems arise when modeling mechanical systems with nonholonomic</br>constraints. In engineering applications it is often required to</br>maintain the mechanical system around a desired configuration. This</br>task is treated as a stabilization problem where the desired</br>configuration is made an asymptotically stable equilibrium point. The</br>control design is carried out on an approximate system. The</br>approximation process yields a nilpotent set of input vector fields</br>which, in a special coordinate system, are homogeneous with respect to</br>a non-standard dilation. Even though the approximation can be given a</br>coordinate-free interpretation, the homogeneous structure is useful to</br>exploit: the feedbacks are required to be homogeneous functions and</br>thus preserve the homogeneous structure in the closed-loop system.</br>The stability achieved is called {\em $\rho$-exponential stability}.</br>The closed-loop system is stable and the equilibrium point is</br>exponentially attractive. This extended notion of exponential</br>stability is required since the feedback, and hence the closed-loop</br>system, is not Lipschitz. However, it is shown that the convergence</br>rate of a Lipschitz closed-loop driftless system cannot be bounded by</br>an exponential envelope.</br><p></br>The synthesis methods generate feedbacks which are smooth on</br>\rminus. The solutions of the closed-loop system are proven to be</br>unique in this case. In addition, the control inputs for many</br>driftless systems are velocities. For this class of systems it is</br>more appropriate for the control law to specify actuator forces</br>instead of velocities. We have extended the kinematic velocity</br>controllers to controllers which command forces and still</br>$\rho$-exponentially stabilize the system.</br><p></br>Perhaps the ultimate justification of the methods proposed in this</br>thesis are the experimental results. The experiments demonstrate the</br>superior convergence performance of the $\rho$-exponential stabilizers</br>versus traditional smooth feedbacks. The experiments also highlight</br>the importance of transformation conditioning in the feedbacks. Other</br>design issues, such as scaling the measured states to eliminate</br>hunting, are discussed. The methods in this thesis bring the</br>practical control of strongly nonlinear systems one step closer.</br><p>rol of strongly nonlinear systems one step closer. <p>)
• Model-Based Estimation of Off-Highway Road Geometry using Single-Axis LADAR and Inertial Sensing  + (This paper applies some previously studied … This paper applies some previously studied extended</br>Kalman filter techniques for planar road geometry</br>estimation to the domain of autonomous navigation of offhighway</br>vehicles. In this work, a clothoid model of the road</br>geometry is constructed and estimated recursively based on</br>road features extracted from single-axis LADAR range measurements.</br>We present a method for feature extraction of the</br>road centerline in the image plane, and describe its application</br>to recursive estimation of the road geometry. We analyze</br>the performance of our method against simulated motion of</br>varied road geometries and against recorded data from previous</br>autonomous navigation runs. Our method accomodates full 6</br>DOF motion of the vehicle as it navigates, constructs consistent</br>estimates of the road geometry with respect to a fixed global</br>reference frame, and requires an estimate of the sensor pose</br>for each range measurement.he sensor pose for each range measurement.)
• Receding Horizon Temporal Logic Planning for Dynamical Systems  + (This paper bridges the advances in compute … This paper bridges the advances in computer science and control to allow automatic synthesis of complex dynamical systems which are guaranteed, by construction, to satisfy the desired properties even in the presence of adversary. The desired properties are expressed in the language of temporal logic. With its expressive power, a wider class of properties than safety and stability can be specified. The resulting system consists of a discrete planner which plans, in the abstracted discrete domain, a set of transitions of the system to ensure the correct behaviors and a continuous controller which continuously implements the plan. For a system with certain structure, we present an approach, based on a receding horizon scheme, to overcome computational difficulties in the synthesis of a discrete planner and allow more complex problems to be solved. allow more complex problems to be solved.)
• Exponential Stabilization of Driftless Nonlinear Control Systems via Time-varying, Homogeneous Feedback  + (This paper brings together results from a … This paper brings together results from a number of different areas in</br>control theory to provide an algorithm for the synthesis of locally</br>exponentially stabilizing control laws for a large class of driftless</br>nonlinear control systems. The exponential stabilization relies on the</br>use of feedbacks which render the closed loop vector field homogeneous</br>with respect to a dilation. These feedbacks are generated from a</br>modification of Pomet's algorithm for smooth feedbacks. Converse</br>Liapunov theorems for time-periodic homogeneous vector fields</br>guarantee that local exponential stability is maintained in the</br>presence of higher order (with respect to the dilation) perturbing</br>terms.</br><p>ect to the dilation) perturbing terms. <p>)
• Real-valued average consensus over noisy quantized channels  + (This paper concerns the average consensus … This paper concerns the average consensus problem with the constraint of quantized communication between nodes. A broad class of algorithms is analyzed, in which the transmission strategy, which decides what value to communicate to the neighbors, can include various kinds of rounding, probabilistic quantization, and bounded noise. The arbitrariness of the transmission strategy is compensated by a feedback mechanism which can be interpreted as a self-inhibitory action. The result is that the average of the nodes state is not conserved across iterations, and the nodes do not converge to a consensus; however, we show that both errors can be made as small as desired. Bounds on these quantities involve the spectral properties of the graph and can be proved by employing elementary techniques of LTI systems analysis.entary techniques of LTI systems analysis.)
• Decentralised minimal-time dynamic consensus  + (This paper considers a group of agents tha … This paper considers a group of agents that aim to reach an agreement on individually measured time-varying signals by local communication. In contrast to static network averaging problem, the consensus we mean in this paper is reached in a dynamic sense. A discrete-time dynamic average consensus protocol can be designed to allow all the agents tracking the average of their reference inputs asymptotically. We propose a minimal-time dynamic consensus algorithm, which only utilises minimal number of local observations of randomly picked node in a network to compute the final consensus signal. Our results illustrate that with memory and computational ability, the running time of distributed averaging algorithms can be indeed improved dramatically using local information as suggested by Olshevsky and Tsitsiklis. as suggested by Olshevsky and Tsitsiklis.)
• Stability and Performance of Non-Homogeneous Multi-Agent Systems on a Graph  + (This paper considers distributed control o … This paper considers distributed control of interconnected multi-agent systems. The dynamics of the individual agents are not required to be homogeneous and the interaction topology is described by an arbitrary directed graph. We derive the sensitivity transfer functions between every pair of agents and we analyze stability and performance of non-homogeneous systems, showing that the low frequency behavior is influenced not only by topology, but also by static gain and poles of the agents.so by static gain and poles of the agents.)
• On Decentralized Classification using a Network of Mobile Sensors  + (This paper considers how a team of mobile … This paper considers how a team of mobile sensors</br>should cooperatively move so as to optimally categorize a</br>single moving target from their noisy sensor readings. The</br>cooperative control procedure is based on the development of</br>a cost function that quantifies the teamâs classification error.</br>The robotsâ motions are then chosen to minimize this function.</br>We particularly investigate the case where the sensor noise and</br>class distributions are Gaussian. In this case, we can derive a</br>duality principle which states that optimal classification will be</br>realized when the covariance of the target estimate is minimized.</br>That is, in this case, optimal estimation leads naturally to</br>optimal classification. We extend previous work to develop a</br>distributed discrete-gradient search algorithm that guides the</br>teamâs location motions for purposes of optimal estimation and</br>classification. The concepts developed are validated through</br>numerical studies.d are validated through numerical studies.)
• Nonlinear Control Methods for Planar Carangiform Robot Fish  + (This paper considers the design of motion … This paper considers the design of motion control algorithms for robot fish. We present modeling, control design, and experimental trajectory tracking results for a planar robotic fish that is propelled using the carangiform style of locomotion. Our experimental apparatus consists of a freely translating and rotating flat plate and a two-link actuated tail. We develop a model for the fish's propulsion that is based on quasi-steady fluid flow. Using this model, we predict system response to sinusoidal motions of the tail joints and</br>compare these predictions to the experimental results. We then propose gaits for forward and turning trajectories and analyze system response under such control strategies. Our models and predictions are verified by experiment.nd predictions are verified by experiment.)
• A Testbed for Nonlinear Flight Control Techniques: The Caltech Ducted Fan  + (This paper considers the fundamental desig … This paper considers the fundamental design and modeling of the Caltech ducted fan.</br>The Caltech ducted fan is a scaled model of the longitudinal axis of a flight vehicle. The</br>purpose of the ducted fan is the research and development of new nonlinear flight guidance</br>and control techniques for Uninhabited Combat Aerial Vehicles. It is shown that critical</br>design relations must be satisfied in order that the ducted fan's longitudinal dynamics</br>behave similar to those of an flight vehicle. Preliminary flight test results illustrate</br>the flying qualities of the ducted fan.te the flying qualities of the ducted fan.)
• Estimation over Communication Networks: Performance Bounds and Achievability Results  + (This paper considers the problem of estima … This paper considers the problem of estimation over</br>communication networks. Suppose a sensor is taking</br>measurements of a dynamic </br>process. However the process needs to be estimated at a</br>remote</br>location connected to the sensor through a network of</br>communication links that drop</br>packets stochastically. We provide a framework for</br>computing the</br>optimal performance in the sense of expected error</br>covariance. Using</br>this framework we characterize the dependency of the</br>performance on</br>the topology of the network and the packet dropping</br>process. For</br>independent and memoryless packet dropping processes we</br>find the</br>steady-state error for some classes of networks and obtain</br>lower and</br>upper bounds for the performance of a general network. We</br>also</br>illustrate how this framework can be used in the synthesis</br>of</br>networks for the purpose of estimation. Finally we find a</br>necessary</br>and sufficient condition for the stability of the estimate</br>error</br>covariance for general networks with spatially correlated</br>and Markov</br>type dropping process. This interesting condition has a</br>max-cut</br>interpretation.ng condition has a max-cut interpretation.)
• A Motion Planner for Nonholonomic Robots  + (This paper considers the problem of motion … This paper considers the problem of motion planning for a car-like robot (i.e., a</br>mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We</br>present a fast and exact planner for our mobile robot model, based upon recursive</br>subdivision of a collision-free path generated by a lower-level geometric planner that</br>ignores the motion constraints. The resultant trajectory is optimized to give a path that</br>is of near-minimal length in its homotopy class. Our claims of high speed are supported by</br>experimental results for implementations that assume a robot moving amid polygonal</br>obstacles. The completeness and the complexity of the algorithm are proven using an</br>appropriate metric in the configuration space R2 x S1 of the robot. This metric is defined</br>by using the length of the shortest paths in the absence of obstacles as the distance</br>between two configurations. We prove that the new induced topology and the classical one</br>are the same. Although we concentration upon the car-like robot, the generalization of</br>these techniques leads to new theoretical issues involving sub-Riemannian geometry and to</br>practical results for nonholonomic motion planning. results for nonholonomic motion planning.)
• Real Time Trajectory Generation for Differentially Flat Systems  + (This paper considers the problem of real t … This paper considers the problem of real time trajectory generation and tracking for</br>nonlinear control systems. We employ a two degree of freedom approach that separates the</br>nonlinear tracking problem into real time trajectory generation followed by local</br>(gain-scheduled) stabilization. The central problem which we consider is how to generate,</br>possibly with some delay, a feasible state space and input trajectory in real time from an</br>output trajectory that is given online. We propose two algorithms that solve the real time</br>trajectory generation problem for differentially flat systems with (possibly non-minimum</br>phase) zero dynamics. One is based on receding horizon point to point steering, the other</br>allows additional minimization of a cost function. Both algorithms explicitly address the</br>tradeoff between stability and performance and we prove convergence of the algorithms for</br>a reasonable class of output trajectories. To illustrate the application of these</br>techniques to physical systems, we present experimental results using a vectored thrust</br>flight control experiment built at Caltech. A brief introduction to differentially flat</br>systems and its relationship with feedback linearization is also included.h feedback linearization is also included.)
• Synthesis of Correct-by-construction Control Protocols for Hybrid Systems Using Partial State Information  + (This paper considers the problem of synthe … This paper considers the problem of synthesizing output-feedback control laws for a class of discrete-time hybrid systems in order for the trajectories of the system to satisfy certain high-level specifications expressed in linear temporal logic. By leveraging ideas from robust interpretation of temporal logic formulas and bounded-error estimation, we identify a subclass of systems for which it is possible to reduce the problem to a state-feedback form. In particular, we use locally superstable hybrid observers to resolve the partial information at the continuous level. This allows us to use recent results in temporal logic planning to synthesize the desired controllers based on two-player perfect- information games. The overall control architecture consists of a hybrid observer, a high-level switching protocol and a low-level continuous controller. We demonstrate the proposed framework in a case study on designing control protocols for an aircraft air management system.ols for an aircraft air management system.)
• Backtracking temporal logic synthesis for uncertain environments  + (This paper considers the problem of synthe … This paper considers the problem of synthesizing correct-by-construction robotic controllers in environments with uncertain but fixed structure. âEnvironmentâ has two notions in this work: a map or âworldâ in which some controlled agent must operate and navigate (i.e. evolve in a configuration space with obstacles); and an adversarial player that selects con- tinuous and discrete variables to try to make the agent fail (as in a game). Both the robot and the environment are subjected to behavioral specifications expressed as an assume-guarantee linear temporal logic (LTL) formula. We then consider how to efficiently modify the synthesized controller when the robot encounters unexpected changes in its environment. The crucial insight is that a portion of this problem takes place in a metric space, which provides a notion of nearness. Thus if a nominal plan fails, we need not resynthesize it entirely, but instead can âpatchâ it locally. We present an algorithm for doing this, prove soundness, and demonstrate it on an example gridworld.nd demonstrate it on an example gridworld.)
• On Quantized Consensus by Means of Gossip Algorithm -- Part II: Convergence Time  + (This paper deals with the distributed aver … This paper deals with the distributed averaging problem over a connected network of agents, subject to a quantization constraint. It is assumed that at each time update, only a pair of agents can update their own numbers in terms of the quantized data being exchanged. The agents are also required to communicate with one another in a stochastic fashion. In the first part of the paper, it was shown that the quantized consensus is reached by means of a stochastic gossip algorithm proposed in a recent paper, for any arbitrary quantization. The current part of the paper considers the expected value of the time at which the quantized consensus is reached. This quantity (corresponding to the worst case) is upper and lower bounded in terms of the topology of the graph, for uniform quantization. In particular, it is shown that these bounds are related to the principal minors of the weighted Laplacian matrix. A convex optimization is also proposed to determine the set of probabilities (used to pick a pair of agents) which leads to the fast convergence of the gossip algorithm. fast convergence of the gossip algorithm.)
• Tuning a synthetic in vitro oscillator using control-theoretic tools  + (This paper demonstrates the effectiveness … This paper demonstrates the effectiveness of sim- ple control-theoretic tools in generating simulation-guided ex- periments on a synthetic in vitro oscillator. A theoretical analysis of the behavior of such system is motivated by high cost, time consuming experiments, together with the excessive number of tuning parameters. A simplified model of the synthetic oscillator is chosen to capture only its essential features. The model is analyzed using the small gain theorem and the theory of describing functions. Such analysis reveals what are the parameters that primarily determine when the system can admit stable oscillations. Experimental verification of the theoretical and numerical findings is carried out and confirms the predicted results regarding the role of production and degradation rates. role of production and degradation rates.)
• TuLiP: A Software Toolbox for Receding Horizon Temporal Logic Planning  + (This paper describes TuLiP, a Python-based … This paper describes TuLiP, a Python-based software tool- box for the synthesis of embedded control software that is provably correct with respect to an expressive subset of lin- ear temporal logic (LTL) specifications. TuLiP combines routines for (1) finite state abstraction of control systems, (2) digital design synthesis from LTL specifications, and (3) receding horizon planning. The underlying digital de- sign synthesis routine treats the environment as adversary; hence, the resulting controller is guaranteed to be correct for any admissible environment profile. TuLiP applies the re- ceding horizon framework, allowing the synthesis problem to be broken into a set of smaller problems, and consequently alleviating the computational complexity of the synthesis procedure, while preserving the correctness guarantee.hile preserving the correctness guarantee.)
• Design of insulating devices for in vitro synthetic circuits  + (This paper describes a synthetic in vitro … This paper describes a synthetic in vitro genetic circuit programmed to work as an insulating device. This circuit is composed of nucleic acids, which can be designed to interact according to user defined rules, and of few proteins that perform catalytic functions. A model of the circuit is derived from first principle biochemical laws. This model is shown to exhibit time-scale separation that makes its output insensitive to downstream time varying loads. Simulation results show the circuit effectiveness and represent the starting point for future experimental testing of the device.future experimental testing of the device.)
• Reduction of Bleed Valve Bandwidth Requirements for Control of Rotating Stall using Continuous Air Injection  + (This paper describes a technique for reduc … This paper describes a technique for reducing the actuator rate</br>requirement in active control of rotating stall and surge on</br>compressors. Actuation of the compressor characteristic, via the use</br>of continuous air injection at the rotor face in a single-stage, low</br>speed axial compressor, has been experimentally verified to provide a</br>method of reducing the actuator rate requirement of bleed valve</br>control of rotating stall. With a compressor rotor frequency of 100</br>Hz, active control of stall with a high speed bleed valve is achieved</br>only when the compressor characteristic is actuated. Furthermore, the</br>experiments show that the bleed valve rate requirement is reduced from</br>approximately 145 Hz to below 10 Hz when the amount of compressor</br>characteristic actuation is increased. Theoretical tools based on a</br>low order model (1-3 states) and simulations based on a reduced order</br>distributed model (37 states) have been developed to estimate the gain</br>and rate requirements of the bleed controller. All of the analytical</br>formulas and simulations share the same qualitative trends with</br>respect to the second and third derivatives of the compressor</br>characteristic function evaluated at the peak, and the experiments.</br>The agreement implies that bleed valve control of rotating stall</br>depends crucially on the rate limit of the bleed valve which in turn</br>depends on both the stable and the unstable part of the compressor</br>characteristic. Actuation of the compressor characteristic is</br>concluded to be a valuable tool in circumventing the rate limitation</br>of bleed valves for control of stall. By combining the compressor</br>characteristic identification tools and the analytic relations,</br>insights for designing a compressor-bleed pair are provided.ning a compressor-bleed pair are provided.)
• Approximate Trajectory Generation for Differentially Flat Systems with Zero Dynamics  + (This paper describes algorithms to generat … This paper describes algorithms to generate trajectories </br>for differentially flat systems with zero dynamics. </br>Zero dynamics in flat systems occur when the flat outputs </br>are not the tracking outputs. This means that the output </br>trajectories can be fully parametrized by the flat outputs, </br>but that there is some additional freedom left. </br>This freedom can be exploited to minimize a cost criterion. </br>We parametrize the differentially </br>flat outputs by basis functions, and solve for the parameters </br>so as to track a prescribed trajectory approximately </br>while minimizing a cost function. </br>We focus on implementation issues and point out the computational </br>cost involved in the various problems.al cost involved in the various problems.)
• Extending Exponential Stabilizers for Nonholonomic Systems from Kinematic Controllers to Dynamic Controllers  + (This paper describes an approach for exten … This paper describes an approach for extending (time-varying)</br>exponential stabilizers for nonholonomic systems from controllers which</br>command input velocity to controllers which command input torques. Due</br>to the nondifferentiable nature of exponential stablizers, additional</br>structure is required in order to ensure that the extended controllers</br>generate continuous control actions. In this paper we show how to</br>extend homogeneous controllers which use a nonstandard dilation adapted</br>to the problem.nstandard dilation adapted to the problem.)