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• 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.)
• Differential Flatness of Mechanical Control Systems: A Catalog of Prototype Systems  + (This paper describes the application of di … This paper describes the application of differential flatness</br>techniques from nonlinear control theory to mechanical (Lagrangian)</br>systems. Systems which are differentially flat have several useful</br>properties which can be exploited to generate effective control</br>strategies for nonlinear systems. For the special case of mechanical</br>control systems, much more geometric information is present and the</br>purpose of this paper is to explore the implications and features of</br>that class of systems. We concentrate on several worked examples</br>which illustrate the general theory and present a detailed catalog of</br>known examples of differentially flat mechanical systems.of differentially flat mechanical systems.)
• Design and Implementation of a Biomolecular Circuit for Tracking Protein Concentration  + (This paper describes the design, modeling, … This paper describes the design, modeling, synthesis and preliminary validation of a protein concentration regulator circuit. The circuit is designed to maintain the level of a target protein to a reference level, specified by the amount of another protein. This is implemented using a single negative feedback loop that inhibited the production of the target protein once its concentration was equal to the reference amount. A mathematical model consisting of a set of ODEs is derived from mass action laws and Hill function approximations of protein production. Steady-state analysis of the model is used to predict parameter sensitivity and experimental behavior. We implemented this circuit in ''E. coli'' using scaffold-based sequestration and transcriptional activation. Preliminary experimental results show the system matching predictions from our model and performing the expected task.ur model and performing the expected task.)
• Interfacing TuLiP with the JPL Statechart Autocoder: Initial progress toward synthesis of flight software from formal specifications  + (This paper describes the implementation of … This paper describes the implementation of an in- terface connecting the two tools : the JPL SCA (Statechart Autocoder) and TuLiP (Temporal Logic Planning Toolbox) to enable the automatic synthesis of low level implementation code directly from formal specifications. With system dynamics, bounds on uncertainty and formal specifications as inputs, TuLiP synthesizes Mealy machines that are correct-by-construction. An interface is built that automatically translates these Mealy machines into UML statecharts. The SCA accepts the UML statecharts (as XML files) to synthesize flight-certified2 implementation code. The functionality of the interface is demonstrated through three example systems of varying com- plexity a) a simple thermostat b) a simple speed controller for an autonomous vehicle and c) a more complex speed controller for an autonomous vehicle with a map-element. In the thermostat controller, there is a specification regarding the desired temperature range that has to be met despite disturbance from the environment. Similarly, in the speed-controllers there are specifications about safe driving speeds depending on sensor health (sensors fail unpredictably) and the map-location. The significance of these demonstrations is the potential circumventing of some of the manual design of statecharts for flight software/controllers. As a result, we expect that less testing and validation will be necessary. In applications where the products of synthesis are used alongside manually designed components, extensive testing or new certificates of correctness of the composition may still be required. of the composition may still be required.)
• Alice: An information-rich autonomous vehicle for high-speed desert navigation  + (This paper describes the implementation an … This paper describes the implementation and testing of Alice, the California Institute of Technology’s entry in the 2005 DARPA Grand Challenge. Alice utilizes a highly networked control system architecture to provide high performance, autonomous driving in unknown en- vironments. Innovations include a vehicle architecture designed for efficient testing in harsh environments, a highly sensory-driven approach to fuse sensor data into speed maps used by real-time trajectory optimization algorithms, health and contingency management algorithms to manage failures at the component and system level, and a software logging and display envi- ronment that enables rapid assessment of performance during testing. The system successfully completed several runs in the National Qualifying Event, but encountered a combination of sens- ing and control issues in the Grand Challenge Event that led to a critical failure after traversing approximately 8 miles.re after traversing approximately 8 miles.)
• A Domain-Specific Language for Reactive Control Protocols for Aircraft Electric Power Systems  + (This paper describes the use of a domain-s … This paper describes the use of a domain-specific language, and an accompanying software tool, in constructing correct- by-construction control protocols for aircraft electric power systems. Given a base topology, the language consists of a set of primitives for standard specifications. The accompanying tool converts these primitives into formal specifica- tions, which are used to synthesize control protocols. We can then use TuLiP, a Python-based software toolbox, to synthesize centralized and distributed controllers. For sys- tems with no time involved in the specifications, this tool also provides an option to output specifications into a SAT-solver compatible format, thus reducing the synthesis problem to a satisfiability problem. We provide the results of our synthesis procedure on a range of topologies.thesis procedure on a range of topologies.)
• Controlling biological networks by time-delayed signals  + (This paper describes the use of time-delay … This paper describes the use of time-delayed feedback to regulate the behavior of biological networks. The general ideas are demonstrated on specific transcriptional regulatory and neural networks. It is shown that robust yet tunable controllers can be constructed that provide the biological systems with model-engineered inputs. The results indicate that time delay modulation may serve as an efficient bio-compatible control tool. an efficient bio-compatible control tool.)
• Receding Horizon Control of a Vectored Thrust Flight Experiment  + (This paper details the application of a co … This paper details the application of a constrained receding horizon control techniques to</br>stabilize an indoor vectored-thrust flight experiment, known as the Caltech Ducted Fan, subjected to step commands. The result of the experiment sheds light on the theoretical stability</br>of the receding horizon control strategy as well as validates some efficient computation techniques for solving nonlinear optimal control problems with constraints. The receding horizon</br>control problem is formulated as a constrained optimal control problem, which was solved with</br>an e±cient computational method developed and implemented by Milam et al., that combines</br>nonlinear control theory, B-spline basis functions, and nonlinear programming. Characteristic</br>issues including non-zero computational times, convergence property, choice of horizon length</br>and terminal cost are discussed. The study confirms the applicability of real-time receding</br>horizon control for constrained systems with fast dynamics.or constrained systems with fast dynamics.)
• Real-Time Trajectory Generation for the Cooperative Path Planning of Multi-Vehicle Systems  + (This paper discusses a Cooperative Path Pl … This paper discusses a Cooperative Path Planning (CPP) design</br>methodology for multi-vehicle systems and a Nonlinear</br>Trajectory Generation (NTG) algorithm. Three scenarios</br>of multi-vehicle tasking are proposed at the CPP framework.</br>The NTG algorithm is, then, used to generate realtime</br>trajectory for desired vehicle activities. Given system</br>dynamics and constraints, the NTG algorithm first finds trajectory</br>curves in a lower dimensional space and, then, parameterizes</br>the curves by the B-spline basis. The coefficients of the B-splines are further solved by the sequential</br>quadratic programming to satisfy the optimization objectives</br>and constraints. The NTG algorithm has been implemented</br>to generate real-time trajectories for a group of</br>cooperative vehicles in the presence of changing missions</br>and constraints.ence of changing missions and constraints.)
• Cooperative Task Planning of Multi-Robot Systems with Temporal Constraints  + (This paper discusses a design methodology … This paper discusses a design methodology of cooperative</br>trajectory generation for multi-robot systems.</br>The trajectory of achieving cooperative tasks, i.e., with</br>temporal constraints, is constructed by a nonlinear trajectory</br>generation (NTG) algorithm. Three scenarios</br>of multi-robot tasking are proposed at the cooperative</br>task planning framework. The NTG algorithm is, then,</br>used to generate real-time trajectory for desired robot</br>activities. Given robot dynamics and constraints, the</br>NTG algorithm first finds trajectory curves in a lower</br>dimensional space and, then, parameterizes the curves</br>by a set of B-spline representations. The coe�cients</br>of the B-splines are further solved by the sequential</br>quadratic programming to satisfy the optimization objectives</br>and constraints. The NTG algorithm has been</br>implemented to generate real-time trajectories for a</br>group of cooperative robots in the presence of spatial</br>and temporal constraints. Finally, an illustrated example</br>of cooperative task planning with temporal constraints</br>is presented.ng with temporal constraints is presented.)
• Low-Observable Nonlinear Trajectory Generation for Unmanned Air Vehicles  + (This paper explores low observability flig … This paper explores low observability flight path planning of unmanned air vehicles (UAVs)</br>in the presence of radar detection systems. The probability of detection model of an aircraft</br>near an enemy radar depends on aircraft attitude, range, and configuration. A detection model</br>is coupled with a simplified aircraft dynamics model. The Nonlinear Trajectory Generation</br>(NTG) software package developed at Caltech is used. The NTG algorithm is a gradient descent</br>optimization method that combines three technologies: Bsplines, output space collocation and</br>nonlinear optimization tools. Implementations are formulated with temporal constraints that</br>allow periods of high observability interspersed with periods of low observability. Illustrative</br>examples of optimized routes for low observability are presented.outes for low observability are presented.)
• A Framework for Low--Observable Tra jectory Generation in the Presence of Multiple Radars  + (This paper explores the problem of finding … This paper explores the problem of finding a real--time optimal tra jectory for unmanned air vehicles (UAV) in order to minimize their probability of detection by opponent multiple radar detection systems. The problem is handled using the Nonlinear Tra jectory Generation (NTG) method developed by Milam et al. The paper presents a formulation of the trajectory generation task as an optimal control problem, where temporal constraints allow periods of high observability interspersed with periods of low observability. This feature can be used strategically to aid in avoiding detection by an opponent radar. The guidance is provided in the form of sampled tabular data. It is then shown that the success of NTG on the proposed low--observable tra jectory generation problem depends upon an accurate parameterization of the guidance data. In particular, such an approximator is desired to have a compact architecture, a minimum number of design parameters, and a smooth continuously--differentiable input-output mapping. Artificial Neural Networks (ANNs) as universal approximators are known to possess these features, and thus are considered here as appropriate candidates for this task. Comparison of ANNs against B-spline approximators is provided, as well. Numerical simulations on multiple radar scenarios illustrate UAV </br>trajectories optimized for both detectability and time.optimized for both detectability and time.)
• Stability Analysis of Interconnected Nonlinear Systems Under Matrix Feedback  + (This paper explores the stability analysis … This paper explores the stability analysis problem for nonlinear systems which have general</br>linear feedback interconnections. Systems are often modeled in this manner in the study of</br>decentralized control because many communication topologies can be modeled and analyzed</br>using connections to graph theory. We present necessary conditions for stability of a classification</br>of interconnected systems, and we give some examples to provide insight into this problem.</br>These conditions are related to positive definiteness of matrices associated with the feedback</br>interconnection, and specialize to the common case where the Laplacian matrix of a graph</br>represents the communication topology of the system. the communication topology of the system.)
• Limits on the network sensitivity function for multi-agent systems on a graph  + (This paper explores the tradeoffs and limi … This paper explores the tradeoffs and limits of performance in feedback control of interconnected multi-agent systems, focused on the network sensitivity functions. We consider the interaction topology described by a directed graph and we prove that the sensitivity transfer functions between every pair of agents, arbitrarily connected, can be derived using a version of the Mason's Direct Rule. Explicit forms for special types of graphs are presented. An analysis of the role of cycles points out that these structures influence and limit considerably the behavior of the system. The more the cycles are equally distributed among the formation, the better performance the system can achieve, but they are always worse than the single agent case. We also prove the networked version of Bode's integral formula, showing that it still holds for multi-agent systems.at it still holds for multi-agent systems.)
• Feedback architectures to regulate flux of components in artificial gene networks  + (This paper focuses on RNA flux regulation … This paper focuses on RNA flux regulation for in vitro synthetic gene networks and considers architectures that can be scaled to an arbitrary number of species. Feedback loops are designed based on negative autoâregulation (which can minimize the potentially harmful amount of molecules not used to form useful products) and crossâactivation (which can maximize the overall output flux): transcription rate matching can be achieved through proper feedback constants; negative feedback is faster and maintains stability. A possible experimen- tal implementation of a three and four genes negative feedback architecture is also numerically studied. architecture is also numerically studied.)
• Control on the Sphere and Reduced Attitude Stabilization  + (This paper focuses on a new geometric appr … This paper focuses on a new geometric approach to fully actuated control</br>systems on the Riemannian manifold S^2. Our control laws exploit the basic</br>and intuitive notions of geodesic direction and of distance between points,</br>and generalize the classical proportional plus derivative feedback (PD)</br>without the need of arbitrary local coordinate charts. Even for the</br>stability analysis, the appropriate Lyapunov function relies upon the notion</br>of distance and its properties. This methodology then applies to spin-axis</br>stabilization of a spacecraft actuated by only two control torques:</br>discarding the rotation about the unactuated axis, a reduced system is</br>considered, whose state is in fact defined on the sphere. For this reduced</br>attitude stabilization problem our approach allows us not only to deal</br>optimally with the inevitable singularity, but also to achieve simplicity,</br>versatility and (coordinate independent) adaptive capabilities.dinate independent) adaptive capabilities.)
• Real-Time Control Experiments for Instruction and Research at Caltech  + (This paper gives a brief introduction to s … This paper gives a brief introduction to some of the experimental</br>facilities at Caltech being used for instruction and research. Two</br>experiments are described: a flight control experiment using a vector</br>thrust engine, and a low-speed, axial flow compressor rig. A common</br>hardware and software infrastructure is used to control these</br>experiments, allowing easy transition from instructional to research</br>use.sition from instructional to research use.)

• Trajectory Generation for Mechanical Systems with Application to Robotic Locomotion  + (This paper gives a survey of current and e … This paper gives a survey of current and emerging techniques for motion control of</br>nonlinear mechanical systems, motivated by applications in robotic locomotion. For this</br>class of systems, internal changes of shape and/or application of body fixed forces are</br>the mechanism by which the robot mov es in its environment and the geometric mechanical</br>properties of the system are crucial in understanding how specific gaits for generating</br>motion can be obtained.its for generating motion can be obtained.)
• Geometric Approaches to Control in the Presence of Magnitude and Rate Saturations  + (This paper gives a survey of some recent r … This paper gives a survey of some recent results on control of systems with magnitude</br>and rate limits, motivated by problems in real-time trajectory generation and tracking for</br>unmanned aerial vehicles. Two problems are considered: stabilization using ``nonlinear</br>wrappers'' to rescale a given control law and real-time trajectory generation using</br>differential flatness. For both problems, simplified versions of the general problem are</br>studied using tools from differential geometry and nonlinear control to give insights into</br>the limitations imposed by magnitude and rate limits and provide insights into</br>constructive solutions to the trajectory generation and tracking problems.ajectory generation and tracking problems.)
• Uncertainty-based Sensor Fusion of Range Data for Real-time Digital Elevation Mapping (RTDEM)  + (This paper introduces a new computationall … This paper introduces a new computationally</br>inexpensive approach to perception and modeling of the</br>environment that allows fusion of sensory range data of</br>various types and fidelities while explicitly taking into account</br>a complete description of uncertainty of the range measurements.</br>This approach makes use of known sensor uncertainty</br>models to create a single 2.5D digital elevation map whose</br>accuracy is robust to sensor noise and spurious data. This</br>approach is particularly suitable for real-time application in</br>high speed and highly unstructured outdoor environments</br>for which reasonably accurate and timely vehicle state estimates</br>are available. Experimental results are presented in</br>which LADAR range measurements and state estimates are</br>combined according to this approach. We provide qualitative</br>comparison to other classes of environment modeling. to other classes of environment modeling.)
• Outer flatness: trajectory generation for a model helicopter  + (This paper introduces the concept of outer … This paper introduces the concept of outer flatness, </br>a derivative of differential flatness. </br>Outer flatness describes a </br>system that can be split </br>in 2 subsytems, a non-flat inner system and a flat outer system. </br>The outputs of the outer system are the tracking outputs of interest. </br>The inputs of the outer system are the outputs of the inner system, </br>and not subject to our direct control. </br>The inputs of the inner system are the real actuator inputs. </br>This system structure is also present in backstepping and dynamic</br>inversion. </br>We present two theorems on exponential and bounded tracking for </br>outer flat systems, based on Lyapunoff arguments. </br>We validate the approach with simulations and experiments </br>on a model helicopter. </br><p>d experiments on a model helicopter. <p>)
• Stabilization of Feedback Systems via Distribution of Delays  + (This paper investigates the results of dis … This paper investigates the results of distributing the delay of a single feedback system. To distribute the delayed feedback, the single delay is replaced by the sum of two distinct delays with the same effective delay. The statistical properties of the new distribution function in the feedback, namely the sum of two delta functions, are used to quantify the effectiveness of delay distribution. We show that the distribution is effective in reducing the magnitude of the open loop transfer function, thereby, decreasing the gain-crossover frequency and improving the phase margin. Finally, inspired by Orosz et al., we demonstrate an example of how these results can be used to design a controller using delays. used to design a controller using delays.)
• Stability of Discrete Time Systems with Stochastically Delayed Feedback  + (This paper investigates the stability of l … This paper investigates the stability of linear systems with stochastic delay in discrete time. Stability of the mean and second moment of the non-deterministic system is determined by a set of deterministic discrete time equations with distributed delay. A theorem is provided that guarantees convergence of the state with convergence of the second moment, assuming the delays are identically independently distributed. The theorems are applied to a scalar equation where the stability of the equilibrium is determined.tability of the equilibrium is determined.)
• Rapid Hover to Forward Flight Transitions for a Thrust Vectored Aircraft  + (This paper investigates the use of efficie … This paper investigates the use of efficient computational algorithms for the</br>computation of a nominal trajectory for fast transition between flight modes. We use</br>differential flatness of an approximate model of the longitudinal dynamics of a thrust</br>vectored aircraft to achieve fast switching between flight modes. We investigate some</br>methods to compensate for the discrepancy between the full aerodynamic model and the</br>approximate flat model, and analyze their performance. Simulations and experimental data</br>for a thrust vectored flight control experiment at Caltech are provided to validate the</br>approach.ech are provided to validate the approach.)
• Robust Nonlinear Control Theory with Applications to Aerospace Vehicles  + (This paper is a very brief outline of an i … This paper is a very brief outline of an invited poster session giving a</br>first-year progress report on a research program with the above title being</br>carried out in the Control and Dynamical Systems (CDS) department at Caltech.</br>This 5-year grant funded by the AFOSR Partnership for Research Excellence</br>Transition (PRET) Program has a special emphasis on transitioning new methods</br>to industrial practice and thus involves a high level of industrial</br>participation. The focus of our program is fundamental research in general</br>methods of analysis and design of complex uncertain nonlinear systems, from</br>creating new mathematical theory to working to make that theory help engineers</br>solve a variety of real industrial problems. Caltech's Control and Dynamical</br>Systems department was created with precisely this goal, which is shared by our</br>industrial collaborators, led by Honeywell. Further details will be available</br>at the poster session.s will be available at the poster session.)
• On Quantized Consensus by Means of Gossip Algorithm -- Part I: Convergence Proof  + (This paper is concerned with the distribut … This paper is concerned with the distributed averaging problem subject to a quantization constraint. Given a group of agents associated with scalar numbers, it is assumed that each pair of agents can communicate with each other with a prescribed probability, and that the data being exchanged between them is quantized. In this part of the paper, it is proved that the stochastic gossip algorithm proposed in a recent paper leads to reaching the quantized consensus. Some important properties of the system in the steady-state (after reaching the consensus) are also derived. The results developed here hold true for any arbitrary quantization, provided the tuning parameter of the gossip algorithm is chosen properly. The expected value of the convergence time bounded in the second part of the paper.e bounded in the second part of the paper.)
• Quantized Consensus via Adaptive Stochastic Gossip Algorithm  + (This paper is concerned with the distribut … This paper is concerned with the distributed averaging problem over a given undirected graph. To enable every vertex to compute the average of the initial numbers sitting on the vertices of the graph, the policy is to pick an edge at random and update the values on its ending vertices based on some rules, but only in terms of the quantized data being exchanged between them. Our recent paper showed that the quantized consensus is reached under a simple updating protocol which deploys a fixed tuning factor. The current paper allows the tuning factor to be time-dependent in order to achieve two goals. First, this makes it possible to study the numerical stability of the protocol with a fixed tuning factor under a small perturbation of this parameter. Furthermore, exploiting a time-varying tuning factor facilitates the implementation of the consensus protocol and pushes the steady state of the system towards an equilibrium point, as opposed to making it oscillatory. The current paper is an important extension of our recent work, which generalizes a finite-dimensional problem toan infinite-dimensional one that is more challenging in nature.al one that is more challenging in nature.)
• Trajectory tracking for fully actuated mechanical systems  + (This paper presents a general framework fo … This paper presents a general framework for the control of mechanical</br>systems with as many inputs as degrees of freedom. The notes of error</br>functions and transport map are introduced to properly define a configuration</br>and velocity error. These are the crucial ingredients in designing a </br>proportional derivative feedback and feedforward control. The proposed</br>approach includes various results on control of manipulators, autonomous</br>vehicles and pointing devices. autonomous vehicles and pointing devices.)
• Analysis and design of a synthetic transcriptional network for exact adaptation  + (This paper presents a mathematical model f … This paper presents a mathematical model for a synthetic transcriptional regulatory network in vitro. This circuit design resembles one of the well-known network motifs, the inco- herent feed-forward loop, in which an activator regulates both a gene and a repressor of the gene. Through mathematical analysis, we show how the circuit can be controlled to demonstrate exact adaptation to input signals.nstrate exact adaptation to input signals.)
• Cross-entropy Temporal Logic Motion Planning  + (This paper presents a method for optimal t … This paper presents a method for optimal trajectory generation for discrete-time nonlinear systems with linear temporal logic (LTL) task specifications. Our approach is based on recent advances in stochastic optimization algorithms for optimal trajectory generation. These methods rely on estimation of the rare event of sampling optimal trajectories, which is achieved by incrementally improving a sampling distribution so as to minimize the cross-entropy. A key component of these stochastic optimization algorithms is determining whether or not a trajectory is collision-free. We generalize this collision checking to e�ciently verify whether or not a trajectory satisfies a LTL formula. Interestingly, this verification can be done in time polynomial in the length of the LTL formula and the trajectory. We also propose a method for e�ciently re-using parts of trajectories that only partially satisfy the specification, instead of simply discarding the entire sample. Our approach is demonstrated through numerical experiments involving Dubins car and a generic point-mass model subject to complex temporal logic task specifications.omplex temporal logic task specifications.)
• Synthesis of Control Protocols for Switched Electrical Power Systems for Commercial Applications with Safety Specifications  + (This paper presents a method for synthesiz … This paper presents a method for synthesizing fault tolerant control protocols for a deterministic discrete event system subject to safety specifications. The system discussed in the paper is modeled as a finite state machine (FSM) and Behavior Tree (BT). The synthesis procedure involves formulating the policy problem as a shortest path dynamic programming problem, and performing a backward search from the desire sates or behavior to the initial configuration. The search is performed over all possible states when applied to the FSM, or over all possible actions when applied to the BT. The resulting strategy minimizes the number of actions performed to meet operational objectives without violating safety conditions. The effectiveness of the procedure on FSMs and BTs is demonstrated through three examples of switched electrical power systems for commercial applications.power systems for commercial applications.)
• Simultaneous Force-Position Control for Grasping Using Flexible Link Manipulators  + (This paper presents a new singular perturb … This paper presents a new singular perturbation approach for analysing</br>flexibility in manipulators. This approach does not treat the flexible</br>manipulator as a perturbation of the rigid manipulator, and therefore,</br>allows for significant amounts of flexibility (beyond the linear</br>range). Analysis based on this approach leads to some provably stable</br>control schemes for the position and force control of flexible-link</br>manipulators. Simulation results are presented for a single flexible</br>manipulator pushing against a wall.exible manipulator pushing against a wall.)
• Recent research in cooperative control of multivehicle systems  + (This paper presents a survey of recent res … This paper presents a survey of recent research in cooperative control of multivehicle systems, using a common mathematical framework to allow different methods to be described in a unified way. The survey has three primary parts: an overview of current applications of cooperative control, a summary of some of the key technical approaches that have been explored, and a description of some possible future directions for research. Specific technical areas that are discussed include formation control, cooperative tasking, spatiotemporal planning, and consensus.g, spatiotemporal planning, and consensus.)
• Dynamic Separation Control in a Low-Speed Asymmetric Diffuser with Varying Downstream Boundary Condition  + (This paper presents an experimental invest … This paper presents an experimental investigation</br>into the effect of a varying downstream boundary</br>condition on dynamic separation control in a twodimensional</br>low-speed asymmetric diffuser. The potential</br>for coupling between the downstream boundary</br>condition and the separation dynamics is relevant,</br>for example, in using separation control to enable</br>more aggressive serpentine aircraft inlets, where</br>the compressor may be close to the separation point.</br>Separation control in the experiment is obtained using</br>spanwise unsteady forcing from a single tangential</br>actuator located directly upstream of the separation</br>point. The downstream boundary condition</br>simulates the dominant quasi-steady and reflection</br>characteristics of a compressor. Although the</br>boundary condition affects the uncontrolled pressure</br>recovery, the optimal forcing frequency is shown to</br>depend only on the mass flow rate and not on either</br>the presence, impedance, or location of the downstream</br>boundary condition. At the conditions tested</br>herein, we therefore conclude that the mechanism</br>underlying dynamic separation control is local in nature,</br>and is not influenced by global system dynamics. not influenced by global system dynamics.)
• Experimental Evaluation of Air Injection for Actuation of Rotating Stall in a Low Speed, Axial Fan  + (This paper presents an experimental invest … This paper presents an experimental investigation of the effects of</br>air injection on the rotating stall instability in a low speed axial</br>compressor. Two experiments concerning air injection were tried. The</br>first experiment used a continuous forcing perpendicular to the flow</br>in the same or opposite direction of the tip velocity. The results</br>show a dramatic difference between the two directions, with opposite</br>direction forcing causing a significant increase in performance, and</br>same direction forcing causing a significant decrease in performance.</br>This result contradicts the Emmons stall propagation model. The</br>second experiment investigated the differences with respect to</br>different frequencies of air injection, with the injector pointed at</br>the fan, parallel to the flow. We found that the change in the</br>compressor characteristic in the unstalled region was highly dependent</br>upon the forcing frequency with the maximum change occurring near the</br>frequency of stall.nge occurring near the frequency of stall.)
• A Constrained Optimization Framework for Wireless Networking in Multi-Vehicle Applications  + (This paper presents an optimization framew … This paper presents an optimization framework for broadcast power-control, specifically addressed</br>at wireless networking issues arising in implementing information flows for multi-vehicle</br>systems. We formulate an optimization problem for the minimization of an aggregate cost subject</br>to a constraint on a quantity we call the geometric connection robustness, which is a locally</br>computable numerical assessment of the robustness of the an information flow to perturbations</br>in position. Our main result is a location-aided distributed power-control algorithm based on</br>a gradient-like optimization scheme. We also use geometric connection robustness to develop a</br>cheap distributed heuristic for the construction of sparse connected information flow.tion of sparse connected information flow.)
• Active Control of Rotating Stall Using Pulsed Air Injection: A Parametric Study on a Low-Speed, Axial Flow Compressor  + (This paper presents preliminary results on … This paper presents preliminary results on the use of low flow, high</br>momentum, pulsed air injectors to control the onset of stall in a</br>low-speed, axial flow compressor. By measuring the unsteady pressures</br>in front of the rotor, the controller determines the magnitude and</br>phase of a stall cell and controls the injection of air in front of</br>the rotor face. Initial experimental results have verified that</br>controller slightly extends the stall point of the compressor and</br>virtually eliminates the hysteresis loop normally associated with</br>stall. An explanation of this effect is proposed based on the</br>quasi-steady effects of air injection on the compressor characteristic</br>curve.on on the compressor characteristic curve.)
• Active Control of an Axial Flow Compressor via Pulsed Air Injection  + (This paper presents the use of pulsed air … This paper presents the use of pulsed air injection to control the onset of rotating</br>stall in a low-speed, axial flow compressor. By measuring the unsteady pressures near the</br>rotor face, a control algorithm determines the magnitude and phase of the first mode of</br>rotating stall and controls the injection of air in the front of the rotor face.</br>Experimental results show that this technique slightly extends the stall point of the</br>compressor and eliminates the hysteresis loop normally associated with rotating stall. A</br>parametric study is used to determine the optimal control parameters for suppression of</br>stall. Analytic results---using a low-dimensional model developed by Moore and Greitzer</br>combined with an unsteady shift in the compressor characteristic to model the</br>injectors---give further insights into the operation of the controller. Based on this</br>model, we show that the behavior of the experiment can be explained as a change in the</br>bifurcation behavior of the system under nonlinear feedback. A higher fidelity simulation</br>model is then used to further verify some of the specific performance characteristics that</br>are observed in experiments.eristics that are observed in experiments.)
• Time-Delayed Feedback Channel Design: Discrete Time H infty Approach  + (This paper proposes a method of improving … This paper proposes a method of improving per- formance of scalar discrete-time systems with substantial delay by adding additional delayed feedback channels (i.e. imposing a distributed delay feedback). The optimal weights for the added feedback channels are found using optimization techniques. In particular, we reduce the H1 norm of the closed loop transfer function with multiple delayed feedback using techniques from static output feedback design. We impose constraints on the feedback gain in order to highlight the effectiveness of the distribution. In this manner, improvement on performance is a result of the distribution and not a change in the overall effective gain. The concept of applying a multiple delayed feedback channel is inspired by biological systems, where substantial delays can be present in feedback control. To show the effectiveness of this idea we apply our method to an example of a scalar genetic autoregulatory network. The constraint on the gain allows one to implement the feedback in a genetic regulatory network without having to change the reaction rates. A possible method of synthesizing such a system in a wet lab is explained in more detail. Finally, stability results indicate the possibility of stabilizing an unstable system with added delayed feedbacks (by adding larger delays). This approach may also be applicable to systems with large delays in which simple controllers are needed due to limitations in computational power. This paper motivates and provides preliminary results towards direct design of purely delay based controllers for network systems with large delays.ers for network systems with large delays.)
• Feasible Trajectories of Linear Dynamic Systems with Inequality Constraints Using Higher-Order Representations  + (This paper proposes a method to determine … This paper proposes a method to determine trajectories of dynamic systems that steer</br>between two end points while satisfying linear inequality constraints arising from limits</br>on states and inputs. The method exploits the structure of the dynamic system written in a</br>higher-order form to explicitly eliminate the state equations. The feasible trajectories</br>of the dynamic system are sought within a characterization with a finite sum of mode</br>functions. In this paper, the linear inequalities on inputs and states are replaced by a</br>finite set of linear inequalities on the mode coefficients. This step changes the problem</br>of trajectory generation into finding a convex polytope enclosed by the linear</br>inequalities on the mode coefficients. A procedure is then developed to efficiently find</br>the vertices of this bounding polytope. It is demonstrated in this paper that this method</br>can generate feasible trajectories of the system in real-time and can quickly update the</br>trajectories as the terminal conditions are changed. The procedure is demonstrated</br>numerically by two examples. The results of one of the examples is implemented in hardware</br>to explore the issues of real-time planning and control. issues of real-time planning and control.)
• Design and performance of in vitro transcription rate regulatory circuit  + (This paper proposes a new synthetic in vit … This paper proposes a new synthetic in vitro circuit that aims at regulating the rate of RNA transcription through positive feedback interactions. This design is dual to a previously synthesized transcriptional rate regulator based on self-repression. Two DNA templates are designed to interact through their transcripts, creating cross activating feedback loops that will equate their transcription rates at steady state. A mathematical model is developed for this circuit, consisting of a set of ODEs derived from the mass action laws and Michaelis--Menten kinetics involving all the present chemical species. This circuit is then compared to its regulatory counterpart based on negative feedback. A global sensitivity analysis reveals the fundamental features of the two designs, by evaluating their equilibrium response to changes in the most crucial parameters of the system.the most crucial parameters of the system.)
• Differentially Flat Systems with Inequality Constraints: An Approach to Real-Time Feasible Trajectory Generation  + (This paper proposes a real-time planning s … This paper proposes a real-time planning scheme and its implementation for a class of dynamic systems. The planner is aimed to satisfy the state equations, the path and actuator constriants, and the given initial and terminal constraints. In order to generate trajectories in real-time, three broad steps are performed: (1) the structure of differentially flat systems is used to explicitly encapsulate the state equations into linear differential constraints in a flat space, and appropriately transform the boundary conditions; (ii) using semi-infinite optimization theory, an inner approximation of nonlinear constraints is made to replace these by a set of linear inequalities in the flat space, i.e., by a polytope; (iii) this polytopic representation of the system that satisfies the state equations and the constraints is then parameterized using basis functions and the planning problem is turned around into solution of a set of linear inequalities in the coefficient space of the basis functions. It is then demonstrated that numerically efficient algorithms can be built to solve the planning problem in real-time. The essence of the approach is demonstrated by two examples: (1) an implementation is performed on a spring-mass-damper system to demonstrate the real-time capability of evasion-pursuit; (ii) a VTOL aircraft is used to illustrate the application of this approach in simulation to nonlinear problems.roach in simulation to nonlinear problems.)