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Nonlinear Control and Modeling of Rotating Stall in an Axial Flow Compressor + (This thesis focuses on understanding the u … This thesis focuses on understanding the use of air injection as a means of controlling rotating stall in an axial flow compressor, involving modeling, dynamical systems analysis, and experimental investigations.The first step towards this understanding was the development of a low order model for air injection control, the starting point of which was the Moore and Greitzer model for axial flow compressors. The Moore and Greitzer model was extended to include the effects of air injection and bifurcation analysis was performed to determine how the closed loop system dynamics are different from those of the open loop system. This low order model was then used to determine the optimal placement of the air injection actuators.Experimental work focused on verifying that the low order model,developed for air injection actuation, qualitatively captured thebehavior of the Caltech compressor rig. Open loop tests were performedto determine how the placement of the air injectors on the rigaffected the performance of the compressor. The positioning of the airinjectors that provided the greatest control authority were used inthe development of air injection controllers for rotating stall. Thecontrollers resulted in complete elimination of the hysteresisassociated with rotating stall. The use of a throttle actuator for thecontrol of the surge dynamics was investigated, and then combined withan air injection controller for rotating stall; the resultingcontroller performed quite well in throttle disturbance rejectiontests.A higher order model was developed to qualitatively match theexperimental results with a simulation. The results of this modelingeffort compared quite well with the experimental results for the openloop behavior of the Caltech rig. The details of how the air injectionactuators affect the compressor flow were included in this model, andthe simulation predicted the same optimal controller that wasdeveloped through experimentation.The development of the higher order model also included the investigation of systematic methods for determining the simulation parameters. Based on experimental measurements of compression system transients, the open loop simulation parameters were identified, including values for the compressor performance characteristic in regions where direct measurements were not possible. These methods also provided information on parameters used in the modeling of the pressure rise delivered by the compressor under unsteady flow conditions.e delivered by the compressor under unsteady flow conditions. )
Control design for hybrid systems with TuLiP: The temporal logic planning toolbox + (This tutorial describes TuLiP, the Tempora … This tutorial describes TuLiP, the Temporal Logic Planning toolbox, a collection of tools for designing controllersfor hybrid systems from specifications in temporal logic. Thetools support a workflow that starts from a description ofdesired behavior, and of the system to be controlled. Thesystem can have discrete state, or be a hybrid dynamicalsystem with a mixed discrete and continuous state space. Thedesired behavior can be represented with temporal logic anddiscrete transition systems. The system description can includeuncontrollable variables that take discrete or continuous values,and represent disturbances and other environmental factorsthat affect the dynamics, as well as communication signals thataffect controller decisions.A control design problem is solved in phases that involveabstraction, discrete synthesis, and continuous feedback control.Abstraction yields a discrete description of system dynamics inlogic. For piecewise affine dynamical systems, this abstractionis constructed automatically, guided by the geometry of the dynamicsand under logical constraints from the specification. Theresulting logic formulae describe admissible discrete behaviorsthat capture both controlled and environment variables. Thediscrete description resulting from abstraction is then conjoinedwith the desired logic specification. To find a controller, thetoolbox solves a game of infinite duration. Existence of a discrete(winning) strategy for the controlled variables in this game is aproof certificate for the existence of a controller for the originalproblem, which guarantees satisfaction of the specification. Thisdiscrete strategy, concretized by using continuous controllers,yields a feedback controller for the original hybrid system. Thetoolbox frontend is written in Python, with backends in C,Python, and Cython.The tutorial starts with an overview of the theory behindTuLiP, and of its software architecture, organized into specifi-cation frontends and backends that implement algorithms forabstraction, solving games, and interfaces to other tools. Then,the main elements for writing a specification for input to TuLiPare introduced. These include logic formulae, discrete transitionsystems annotated with predicates, and hybrid dynamical systems,with linear or piecewise affine continuous dynamics. Theworking principles of the algorithms for predicate abstractionand discrete game solving using nested fixpoints are explained,by following the input specification through the various transformationsthat compile it to a symbolic representation thatscales well to solving large games. The tutorial concludeswith several design examples that demonstrate the toolbox’scapabilities.at demonstrate the toolbox’s capabilities.)
Nonholonomic Mechanical Systems with Symmetry + (This work develops the geometry and dynami … This work develops the geometry and dynamics of mechanical systems with nonholonomicconstraints and symmetry from the perspective of Lagrangian mechanics and with a view tocontrol theoretical applications. The basic methodology is that of geometric mechanicsapplied to the formulation of Lagrange d'Alembert, generalizing the use of connections andmomentum maps associated with a given symmetry group to this case. We begin by formulatingthe mechanics of nonholonomic systems using an Ehresmann connection to model theconstraints, and show how the curvature of this connection enters into Lagrange'sequations. Unlike the situation with standard configuration space constraints, thepresence of symmetries in the nonholonomic case may or may not lead to conservation laws.However, the momentum map determined by the symmetry group still satisfies a usefuldifferential equation that decouples from the group variables. This momentum equation,which plays an important role in control problems, involves parallel transport operatorsand is computed explicitly in coordinates. An alternative description using a ``bodyreference frame'' relates part of the momentum equation to the components of theEuler-Poincar\'{e} equations along those symmetry directions consistent with theconstraints. One of the purposes of this paper is to derive this evolution equation forthe momentum and to distinguish geometrically and mechanically the cases where it isconserved and those where it is not. An example of the former is a ball or vertical diskrolling on a flat plane and an example of the latter is the snakeboard, a modified versionof the skateboard which uses momentum coupling for locomotion generation. We construct asynthesis of the mechanical connection and the Ehresmann connection defining theconstraints, obtaining an important new object we call the nonholonomic connection. Whenthe nonholonomic connection is a principal connection for the given symmetry group, weshow how to perform Lagrangian reduction in the presence of nonholonomic constraints,generalizing previous results which only held in special cases. Several detailed examplesare given to illustrate the theory.amples are given to illustrate the theory.)
Motion Planning with Wireless Network Constraints + (This work discusses feasibility aspects of … This work discusses feasibility aspects of motion planning forgroups of agents connected by a range-constrained wirelessnetwork. Specifically, we address the difficulties encounteredwhen trajectories are required to preserve the connectedness ofthe network. The analysis utilizes a quantity called theconnectivity robustness of the network, which can becalculated in a distributed fashion, and thus is applicable todistributed motion planning problems arising in control of vehiclenetworks. Further, these results show that network constraintsposed as connectivity robustness constraints have minimal impacton reachability, provided that an appropriate topology controlalgorithm is implemented. This contrasts with more naiveapproaches to connectivity maintenance, which can significantlyreduce the reachable set.an significantly reduce the reachable set.)
Dynamic Consensus for Mobile Networks + (This work examines several dynamical aspec … This work examines several dynamical aspects of average consensusin mobile networks. The results herein allow consensus on generaltime-varying signals, and allow tracking analysis using standardfrequency-domain techniques. Further, the frequency-domainanalysis naturally inspires a robust small-gain version of thealgorithm, which tolerates arbitrary non-uniform time delays.Finally, we show how to exploit a dynamical conservation propertyin order to ensure consensus tracking despite splitting andmerging of the underlying mobile network. merging of the underlying mobile network.)
The Mechanics and Control of Robotic Locomotion with Applications to Aquatic Vehicles + (This work illuminates a theory of locomoti … This work illuminates a theory of locomotion rooted in geometric mechanics and nonlinear control. We regard the internal configuration of a deformable body, together with its position and orientation in ambient space, as a point in a trivial principal fiber bundle over the manifold of body deformations. We obtain connections on such bundles which describe the nonholonomic constraints, conservation laws, and force balances to which certain propulsors are subject, and construct and analyze control-affine normal forms for different classes of systems. We examine the applicability of results involving geometric phases to the practical computation of trajectories for systems described by single connections. We propose a model for planar carangiform swimming based on reduced Euler-Lagrange equations for the interaction of a rigid body and an incompressible fluid, accounting for the generation of thrust due to vortex shedding through controlled coupling terms. We investigate the correct form of this coupling experimentally with a robotic propulsor, comparing its observedbehavior with that predicted numerically. behavior with that predicted numerically.)
Distributed Sensor Fusion Using Dynamic Consensus + (This work is an extension to a companion p … This work is an extension to a companion paper describingconsensus-tracking for networked agents, and shows how thoseresults can be applied to obtain least-squares fused estimatesbased on spatially distributed measurements. This mechanism isvery robust to changes in the underlying network topology andperformance, making it an interesting candidate for sensor fusionon autonomous mobile networks. We conclude with an example of apreliminary application to distributed Kalman Filtering using theproposed technique, illustrating the dependence of the performanceon the structure of the underlying network.n the structure of the underlying network.)
Computing Augmented Finite Transition Systems to Synthesize Switching Protocols for Polynomial Switched Systems + (This work is motivated by the problem of s … This work is motivated by the problem of synthe- sizing mode sequences for continuous-time polynomial switched systems in order to guarantee that the trajectories of the system satisfy certain high-level specifications expressed in linear temporal logic. We use augmented finite transition systems as abstract models of continuous switched systems. Augmented finite transition systems are equipped with liveness properties that can be used to enforce progress in accordance with the underlying dynamics. We then introduce abstraction and refinement relations that induce a preorder on this class of finite transition systems. By construction, the resulting pre-order respects the feasibility (i.e., realizability) of the synthesis problem. Hence, existence of a discrete switching strategy for one of these abstract finite transition systems guarantees the existence of a mode sequence for the continuous system such that all of its trajectories satisfy the specification. We also present an algorithm, which can be implemented using sum-of-squares based relaxations, to compute such high fidelity abstract models in a computationally tractable way. Finally, these ideas are illustrated on an example.these ideas are illustrated on an example.)
Synthesis from multi-paradigm specifications + (This work proposes a language for describi … This work proposes a language for describing reactive synthesis problems that integrates imperative and declarative elements. The semantics is defined in terms of two-player turn-based infinite games with full information. Currently, synthesis tools accept linear temporal logic (LTL) as input, but this description is less structured and does not facilitate the expression of sequential constraints. This motivates the use of a structured programming language to specify synthesis problems. Transition systems and guarded commands serve as imperative constructs, expressed in a syntax based on that of the modeling language Promela. The syntax allows defining which player controls data and control flow, and separating a program into assumptions and guarantees. These notions are necessary for input to game solvers. The integration of imperative and declarative paradigms allows using the paradigm that is most appropriate for expressing each requirement. The declarative part is expressed in the LTL fragment of generalized reactivity(1), which admits efficient synthesis algorithms. The implementation translates Promela to input for the Slugs synthesizer and is written in Python.lugs synthesizer and is written in Python.)
Symbolic construction of GR(1) contracts for systems with full information + (This work proposes a symbolic algorithm fo … This work proposes a symbolic algorithm for the construction of assume-guarantee specifications that allow multiple agents to coop- erate. Each agent is assigned goals expressed in a fragment of linear temporal logic known as gener- alized Streett with one pair, GR(1). These goals may be unrealizable, unless each agent makes additional assumptions, about the behavior of other agents. The algorithm constructs a con- tract among the agents, in that only the infinite behavior of the given goals is constrained, known as liveness, not the finite one, known as safety. This defers synthesis to a later stage of refinement, modularizing the design process. We prove that there exist GR(1) games that do not admit any GR(1) contract. For this reason, we formulate contracts with nested GR(1) properties and auxiliary communication variables, and prove that they always exist. The algorithmâs fixpoint structure is similar to GR(1) synthesis, enjoying time complexity polynomial in the number of states, and linear in number of recurrence goals. and linear in number of recurrence goals.)
A modal interface contract theory for guarded input/output automata with an application in traffic system design + (To contribute to efforts of bringing forma … To contribute to efforts of bringing formal design-by-contract methods to hybrid systems, we introduce a variant of modal interface contract theory based on input/output automata with guarded transitions. We present an algebra of operators for interface composition, contract composition, contract conjunction, contract refinement and some theorems demonstrating that our contract object has reasonably universal semantics. As an application, we apply our framework to the design of a networked control systems of traffic.of a networked control systems of traffic.)
Managing information in networked and multi-agent control systems + (Traditional feedback control systems give … Traditional feedback control systems give little attention to issues associated with the flow of information through the feedback loop. Typically implemented with dedicated communication links that deliver nearly precise, reliable, and non-delayed information, researchers have not needed to concern themselves with issues related to quantized, delayed, and even lost information. With the advent of newer technologies and application areas that pass information through non-reliable networks, these issues cannot be ignored. In recent years the field of Networked Control Systems (NCS) has emerged to describe situations where these issues are present. The research in this field focuses on quantifying performance degradations in the presence of network effects and proposing algorithms for managing the information flow to counter those negative effects. In this thesis I propose and analyze algorithms for managing information flow for several Networked Control Systems scenarios: state estimation with lossy measurement signals, using input buffers to reduce the frequency of communication with a remote plant, and performing state estimation when control signals are transmitted to a remote plant via a lossy communication link with no acknowledgement signal at the estimator. Multi-agent coordinated control systems serve as a prime example of an emerging area of feedback control systems that utilize feedback loops with information passed through possibly imperfect communication networks. In these systems, agents use a communication network to exchange information in order to achieve a desired global ob jective. Hence, managing the information flow has a direct impact on the performance of the system. I also explore this area by focusing on the problem of multi-agent average consensus. I propose an algorithm based on a hierarchical decomposition of the communication topology to speed up the time to convergence. For all these topics I focus on designing intuitive algorithms that intelligently manage the information flow and provide analysis and simulations to illustrate their effectiveness.lations to illustrate their effectiveness.)
Observability and Local Observer Construction for Unknown Parameters in Linearly and Nonlinearly Parameterized Systems + (Using geometric concepts from observabilit … Using geometric concepts from observability theory for nonlinear systems, we propose an approach for parameter estimation for linearly and nonlinearly parameterized systems that does not rely on persistence of excitation conditions. The proposed approach relies on extending a parameter estimation problem to a state estimation problem by introducing the parameters as auxiliary state variables. Applying tools from geometric nonlinear control theory we give an observability check for parameters, and, in case the parameters are observable, we provide a constructive way to design a local parameter observer with established speed of convergence.er with established speed of convergence.)
Segmentation of Human Motion into Dynamics Based Primitives with Application to Drawing Tasks + (Using tools from dynamical systems and sys … Using tools from dynamical systems andsystems identification we develop a framework for the study of decomposition ofhuman motion. The objective is understanding human motion by decomposing it into a sequence of elementary building blocks, which we refer to as movemes, that belong to a known alphabet of dynamical systems.We develop classification and segmentation algorithms with error analysis and we test them on human drawing data.s and we test them on human drawing data.)
Decomposition of Human Motion into Dynamics Based Primitives with Application to Drawing Tasks + (Using tools from dynamical systems and sys … Using tools from dynamical systems and systems identiﬁcation we develop a framework for the studyof primitives for human motion, which we refer to as movemes. The objective is understanding humanmotion by decomposing it into a sequence of elementary building blocks that belong to a known alphabetof dynamical systems. In this work we address the problem of deﬁning conditions under whichcollections of signals are well-posed according to a dynamical model class M and then can generatemovemes. Based on the assumption of well-posedness, we develop segmentation and classiﬁcation algorithmsin order to reduce a complex activity into the sequence of movemes that have generated it.Using examples we show that the deﬁnition of well-posedness can be applied in practice and showanalytically that the proposed algorithms are robust with respect to noise and model uncertainty. Wetest our ideas on data sampled from ﬁve human subjects who were drawing ﬁgures using a computermouse. Our experiments show that we are able to distinguish between movemes and recognize themeven when they take place in activities containing more than one moveme at a time.)
Primitives for Human Motion: A Dynamical Approach + (Using tools from dynamical systems theory … Using tools from dynamical systems theory and systems identification theory we develop the study of primitives for human motion which we refer to as movemes. We introduce basic definitions of dynamical independence of LTI systems and segmentability of signals and, for two dimensional motions, we develop classification and segmentation algorithms. We test our ideas on data sampled from four human subjects who were engaged in a simple real-life activity including two movemes. Our experiments show that we are able to distinguish between the two movemes and recognise them even when they take place in an activity containing more than one moveme.place in an activity containing more than one moveme.)
Information Flow and Cooperative Control of Vehicle Formations + (Vehicles in formation often lack global in … Vehicles in formation often lack global information regarding the state ofall the vehicles, a deficiency which can lead to instability and poor performance. Inthis paper, we demonstrate how exchange of minimal amounts of information betweenvehicles can be designed to realize a dynamical system which supplies each vehicle witha shared reference trajectory. When the information flow law is placed in the controlloop, a separation principle is proven which guarantees stability of the formation andconvergence of the information flow law regardless of the information flow topology.gardless of the information flow topology.)
Discrete State Estimators for Systems on a Lattice + (We address the problem of estimating discr … We address the problem of estimating discrete variables in a class of deterministictransition systems where the continuous variables are available for measurement. Thissimplified scenario has practical interest, for example, in the case of decentralized multi-robotsystems. In these systems, the continuous variables represent physical quantities such as theposition and velocity of a robot, while discrete variables may represent the state of the logicalsystem that is used for control and coordination. We propose a novel approach to theestimation of discrete variables using basic lattice theory that overcomes some of the severecomplexity issues encountered in previous work. We show how to construct the proposedestimator for a multi-robot system performing a cooperative assignment task. performing a cooperative assignment task.)
On the Control of Jump Linear Markov Systems with Markov State Estimation + (We analyze a jump linear Markov system bei … We analyze a jump linear Markov system being stabilized using a zero-order hold controller. We consider the case when the Markov state is associated with the probability distribution of a measured variable. We assume that the Markov state is not known, but rather is being estimated based on the observations of the variable. We present conditions for the stability of such a system and also solve the optimal LQR control problem for the case when the state estimate update uses only the last observation value. In particular we consider a suboptimal causal version of the Viterbi estimation algorithm and show that a separtion property does not hold between the optimal control and the Markov state estimate. Some simple examples are also presented.. Some simple examples are also presented.)
Stability Analysis of Stochastically Varying Formations of Dynamic Agents + (We analyze a network of dynamic agents whe … We analyze a network of dynamic agents where thetopology of the network specifies the informationflow between the agents. We present an analysismethod for such a system for both consensus andformation stabilization problems. We consider thecase of agent dynamics being a single integrator inmore detail to show the general features introducedby the information flow. Then we show that themethod of analysis can be extended to more general cases of complicated agent dynamics, non-ideallinks for information flow, etc. We also consider thecase when the topology of the network is changingover time. The focus of the paper is on obtainingconditions for the stability of the formation thatcan be checked in a decentralized way. Some simple examples are also presented.. Some simple examples are also presented.)
Approximate Distributed Kalman Filtering in Sensor Networks with Quantifiable Performance + (We analyze the performance of an approxima … We analyze the performance of an approximate distributed Kalman filter proposedin recent work on distributed coordination. This approach todistributed estimation is novel in that it admits a systematicanalysis of its performance as various network quantities such asconnection density, topology, and bandwidth are varied. Our maincontribution is a frequency-domain characterization of thedistributed estimator's steady-state performance; this is quantified in termsof a special matrix associated with the connection topology calledthe graph Laplacian, and also the rate of message exchangebetween immediate neighbors in the communication network.te neighbors in the communication network.)
Control Over a Network: Using Actuation Buffers to Reduce Transmission Frequency + (We consider a discrete time linear feedbac … We consider a discrete time linear feedback control system with additive noise where the control signals are to be sent across a data link from the controller to the actuators. Due to network constraints it is desired to reduce the transmission frequency of the control signals. We show that by including a finite sequence of predicted control signals in each communication packet the frequency of transmission can be reduced by transmitting only when the previously sent sequence has run out. The price to pay is that the closed loop error will increase. We introduce a novel communication protocol, which we call Input Difference Transmission Scheme (IDTS), which transmits control packets when the difference between the newly computed control sequence and the predicted control sequence previously transmitted is larger than a certain thresh- old. This threshold is a design parameter and we show how the closed loop behavior varies with this threshold. Simulation results are provided to augment the theory and show how the protocol works.e theory and show how the protocol works.)
Parametric Delay-margin Maximization of Consensus Network Using Local Control Scheme + (We consider a network of identical agents … We consider a network of identical agents with arbitrary linear time-invariant (LTI) dynamics such that the network reaches consensus asymptotically. Uniform time delay is taken into account in the communication channels. The goal of this paper is to maximize the delay (so-called delay margin) that the system can tolerate before becoming unstable by implementing a low-order controller to a single agent. A parametric design method is investigated to guarantee the stability and consensusability. The set of all feasible low-order controllers based on the frequency response data is characterized by combining the argument principle and the generalized Nyquist criterion. Based on this, the algorithm of computing the delay margin is proposed for a given controlled agent. By combining all the possible margins for each controlled agent, we then can obtain the maximal delay margin for the whole network and the corresponding local controller.rk and the corresponding local controller.)
Linear System Identifiability from Distributional and Time Series Data + (We consider identifiability of linear syst … We consider identifiability of linear systems driven by white noise using a combination of distributional and time series measurements. Specifically, we assume that the system has no control inputs available and can only be observed at stationarity. The user is able to measure the full stationary state distribution as well as observe time correlations for small subsets of the state. We formulate theoretical conditions on identifiability of parameters from distributional information alone. We then give a sufficient condition and an effective necessary condition for identifiability using a combination of distributional and time series measurements. We illustrate the ideas with some simple examples as well as a biologically inspired example of a transcription and degradation process.f a transcription and degradation process.)
Robot Navigation in Dense Human Crowds: the Case for Cooperation + (We consider mobile robot navigation in den … We consider mobile robot navigation in dense human crowds. In particular, we explore two questions. Can we design a navigation algorithm that encourages humans to coop- erate with a robot? Would such cooperation improve navigation performance? We address the first question by developing a probabilistic predictive model of cooperative collision avoidance and goal-oriented behavior. Specifically, this model extends the recently introduced interacting Gaussian processes approach to the case of multiple goals and stochastic movement duration. We answer the second question by empirically validating our model in a natural environment (a university cafeteria), and in the process, carry out the first extensive quantitative study of robot navigation in dense human crowds (completing 488 runs). The âmultiple goalâ interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities near 1 person/m2, while a state of the art noncooperative planner exhibits unsafe behavior more than 3 times as often as our planner. Furthermore, a reactive planner based on the âdynamic windowâ approachâwidely used for robotic tour guide experimentsâfails for crowd densities above 0.55 people/m2. We conclude that a cooperation model is critical for safe and efficient robot navigation in dense human crowds.nt robot navigation in dense human crowds.)

(We consider optimal control for a system subject to temporal logic const)

Optimal Control with Weighted Average Costs and Temporal Logic Specifications + (We consider optimal control for a system s … We consider optimal control for a system subject to temporal logic constraints. We minimize a weighted average cost function that generalizes the commonly used average cost function from discrete-time optimal control. Dynamic programming algorithms are used to construct an optimal trajectory for the system that minimizes the cost function while satisfying a temporal logic specification. Constructing an optimal trajectory takes only polynomially more time than constructing a feasible trajectory. We demonstrate our methods on simulations of autonomous driving and robotic surveillance tasks.us driving and robotic surveillance tasks.)
Bootstrapping bilinear models of robotic sensorimotor cascades + (We consider the bootstrapping problem, whi … We consider the bootstrapping problem, which consists in learning a model of the agent's sensors and actuators starting from zero prior informa- tion, and we take the problem of servoing as a cross-modal task to validate the learned models. We study the class of sensors with bilinear dynamics, for which the derivative of the observations is a bilinear form of the control commands and the observations themselves. This class of models is simple, yet general enough to represent the main phenomena of three representative sensors (field sampler, camera, and range-finder), apparently very different from one another. It also allows a bootstrapping algorithm based on Hebbian learning, and a simple bioplausible control strategy. The convergence proper- ties of learning and control are demonstrated with extensive simulations and by analytical arguments.e simulations and by analytical arguments.)
Receding Horizon Control of Multi-Vehicle Formations: A Distributed Implementation + (We consider the control of dynamically dec … We consider the control of dynamically decoupledsubsystems whose state vectors are coupled in the costfunction of a finite horizon optimal control problem. For agiven cost structure, we generate distributed optimal controlproblems for each subsystem and establish that a distributedreceding horizon implementation is asymptotically stabilizing.The communication requirements at each recedinghorizon update include the exchange of the previous optimalcontrol trajectory between subsystems with coupling inthe cost function. The key requirements for stability are thateach distributed optimal control not deviate too far from theprevious one, and that the receding horizon updates happensufficiently fast. A simulation example of multi-vehicleformation stabilization is provided.hicle formation stabilization is provided.)
Distributed Receding Horizon Control with Applications to Multi-Vehicle Formation Stabilization + (We consider the control of interacting sub … We consider the control of interacting subsystems whose dynamics and constraintsare uncoupled, but whose state vectors are coupled non-separably in a single centralizedcost function of a finite horizon optimal control problem. For a given centralizedcost structure, we generate distributed optimal control problems for each subsystemand establish that the distributed receding horizon implementation is asymptoticallystabilizing. The communication requirements between subsystems with coupling in thecost function are that each subsystem obtain the previous optimal control trajectory ofthose subsystems at each receding horizon update. The key requirements for stabilityare that each distributed optimal control not deviate too far from the previous optimalcontrol, and that the receding horizon updates happen sufficiently fast. The theory isapplied in simulation for stabilization of a formation of vehicles. stabilization of a formation of vehicles.)
Multi-dimensional state estimation in adversarial environment + (We consider the estimation of a vector sta … We consider the estimation of a vector state based on m measurements that can be potentially manipulated by an adversary. The attacker is assumed to have limited resources and can only manipulate up to l of the m measurements. However, it can the compromise measurements arbitrarily. The problem is formulated as a minimax optimization, where one seeks to construct an optimal estimator that minimizes the âworst-caseâ error against all possible manipulations by the attacker and all possible sensor noises. We show that if the system is not observable after removing 2l sensors, then the worst-case error is infinite, regardless of the estimation strategy. If the system remains observable after removing arbitrary set of 2l sensor, we prove that the optimal state estimation can be computed by solving a semidefinite programming problem. A numerical example is provided to illustrate the effectiveness of the proposed state estimator.ctiveness of the proposed state estimator.)
Risk-aware motion planning for automated vehicle among human-driven cars + (We consider the maneuver planning problem … We consider the maneuver planning problem for automated vehicles when they share the road with human- driven cars and interact with each other using a finite set of maneuvers. Each maneuver is calculated considering input constraints, actuator disturbances and sensor noise, so that we can use a maneuver automaton to perform high-level planning that is robust against low-level effects. In order to model the behavior of human-driven cars in response to the intent of the automated vehicle, we use control improvisation to build a probabilistic model. To accommodate for potential mismatches between the learned human model and human driving behaviors, we use a conditional value-at-risk objective function to obtain the optimal policy for the automated vehicle. We demonstrate through simulations that our motion planning framework allows an automated vehicle to exploit human behaviors with different levels of robustness.viors with different levels of robustness.)
A bio-plausible design for visual attitude stabilization + (We consider the problem of attitude stabil … We consider the problem of attitude stabilization using exclusively visual sensory input, and we look for a solution which can satisfy the constraints of a ``bio-plausible'' computation. We obtain a PD controller which is a bilinear form of the goal image, and the current and delayed visual input. Moreover, this controller can be learned using classic neural networks algorithms. The structure of the resulting computation, derived from general principles by imposing a bilinear computation, has striking resemblances with existing models for visual information processing in insects (Reichardt Correlators and lobula plate tangential cells). We validate the algorithms using faithful simulations of the fruit fly visual input.simulations of the fruit fly visual input.)
Consensus Seeking Using Multi-Hop Relay Protocol + (We consider the problem of average consens … We consider the problem of average consensus seeking in networked multi-agent systems. Based on local information and a simple distributed algorithm, states of all agents automatically converge to the average value of the initial conditions, where the convergence speed is determined by the algebraic connectivity of the underlying communication network. In order to achieve an average consensus quickly, we propose a new type of consensus protocol, multi-hop relay protocol, in which each agent expands its knowledge by employing multi-hop communication links. We explicitly show that multi-hop relay protocol increases the convergence speed without physically changing the network topology. Moreover, accumulated delays along communication links are discussed. We show that, for multi-hop relay protocol, the faster the protocol converges, the more sensitive it is to the delay. This tradeoff is identified when we investigate the stable delay margin using frequency sweep method.delay margin using frequency sweep method.)
Data Transmission over Networks for Estimation and Control + (We consider the problem of controlling a l … We consider the problem of controlling a linear time invariant process when the controller is located at a location remote from where the sensor measurements are being generated. The communication from the sensor to the controller is supported by a communication network with arbitrary topology composed of analog erasure channels. Using a separation principle, we prove that the optimal LQG controller consists of an LQ optimal regulator along with an estimator that estimates the state of the process across the communication network mentioned above. We then determine the optimal information processing strategy that should be followed by each node in the network so that the estimator is able to compute the best possible estimate in the minimum mean squared error sense. The algorithm is optimal for any packet-dropping process and at every time step, even though it is recursive and hence requires a constant amount of memory, processing and transmission at every node in the network per time step. For the case when the packet drop processes are memoryless and independent across links, we analyze the stability properties and the performance of the closed loop system. The algorithm is an attempt to escape the more commonly used viewpoint of treating a network of communication links as a single end-to-end link with the probability of successful transmission determined by some measure of the reliability of the network.measure of the reliability of the network.)
Distributed Power Allocation for Vehicle Management Systems + (We consider the problem of designing distr … We consider the problem of designing distributed control protocols -for aircraft vehicle management systems- that cooperatively allocate electric power while meeting certain higher level goals and requirements, and dynamically reacting to the changes in the internal system state and external environment. A decentralized control problem is posed where each power distribution unit is equipped with a controller that implements a local protocol to allocate power to a certain subset of loads. We use linear temporal logic as the specification language for describing correct behaviors of the system (e.g., safe operating conditions) as well as the admissible dynamic behavior of the environment due to, for example, wind gusts and changes in system health. We start with a global specification and decompose it into local ones. These decompositions allow the protocols for each local controller to be separately synthe- sized and locally implemented while guaranteeing the global specifications to hold. Through a design example, we show that by refining the interface rules between power distribution units, it is possible to reduce the total power requirement.ble to reduce the total power requirement.)
Risk-Averse Planning Under Uncertainty + (We consider the problem of designing polic … We consider the problem of designing policies for partially observable Markov decision processes (POMDPs) with dynamic coherent risk objectives. Synthesizing risk-averse optimal policies for POMDPs requires infinite memory and thus undecidable. To overcome this difficulty, we propose a method based on bounded policy iteration for designing stochastic but finite state (memory) controllers, which takes advantage of standard convex optimization methods. Given a memory budget and optimality criterion, the proposed method modifies the stochastic finite state controller leading to sub-optimal solutions with lower coherent risk.ptimal solutions with lower coherent risk.)
Risk-Averse Decision Making Under Uncertainty + (We consider the problem of designing polic … We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigationumerical experiments on a rover navigatio)
Constrained risk-averse Markov decision processes + (We consider the problem of designing polic … We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigation problem involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent risk measures.lue-at-risk (EVaR) coherent risk measures.)
Dynamic State Estimation in Distributed Aircraft Electric Control Systems via Adaptive Submodularity + (We consider the problem of estimating the … We consider the problem of estimating the discrete state of an aircraft electric system under a distributed control architecture through active sensing. The main idea is to use a set of controllable switches to reconfigure the system in order to gather more information about the unknown state. By adaptively making a sequence of reconfiguration decisions with uncertain outcome and by correlating the measurements and prior information to make the next decision, we aim to reduce the uncertainty. A greedy strategy is developed that maximizes the one-step expected uncertainty reduction. By exploiting recent results on adaptive submodularity, we give theoretical guarantees on the worst-case performance of the greedy strategy. We apply the proposed method in a fault de- tection scenario where the discrete state captures possible faults in various circuit components. In addition, simple abstraction rules are proposed to alleviate state space explosion and to scale up the strategy. Finally, the efficiency of the proposed method is demonstrated empirically on different circuits.strated empirically on different circuits.)
Efficient local validation of partially ordered models via Baysian directed sampling + (We consider the problem of estimating the … We consider the problem of estimating the subset of test conditions under which a simplified model—or set of simplified models—accurately approximates the behavior of a true system. We approach the problem by proposing a compact set of possible test conditions, and an unknown but samplable continous validity function over that set that quantifies the accuracy of the model under each possible condition. We propose a novel Bayes estimator that optimally directs function sampling to greedily minimize the expected posterior misclassification rate of the valid set, which we call minimum posterior misclassification sampling (GP-MPM), and we show that the the method can be extended to approximate the valid sets of a partially ordered set of models, with sample complexity growing sublinearly with the number of models. In testing against a safety-focused model, we show that the algorithm’s estimated valid set approaches the true valid set much more quickly than undirected sampling, even with small sample sizes.ed sampling, even with small sample sizes.)
Motion planning in observations space with learned diffeomorphism models + (We consider the problem of planning motion … We consider the problem of planning motions in observations space, based on learned models of the dynamics that associate to each action a diffeomorphism of the observations domain. For an arbitrary set of diffeomorphisms, this problem must be formulated as a generic search problem. We adapt established algorithms of the graph search family. In this scenario, node expansion is very costly, as each node in the graph is associated to an uncertain diffeomorphism and corresponding predicted observations. We describe several improvements that ameliorate performance: the introduction of better image similarities to use as heuristics; a method to reduce the number of expanded nodes by preliminarily identifying redundant plans; and a method to pre-compute composite actions that make the search efficient in all directions.ke the search efficient in all directions.)
A bio-plausible design for visual pose stabilization + (We consider the problem of purely visual p … We consider the problem of purely visual pose stabilization (also known as servoing) of a second-order rigid- body system with six degrees of freedom: how to choose forces and torques, based on the current view and a memorized goal image, to steer the pose towards a desired one. Emphasis has been given to the bio-plausibility of the computation, in the sense that the control laws could be in principle implemented on the neural substrate of simple insects. We show that stabilizing laws can be realized by bilinear/quadratic operations on the visual input. This particular computational structure has several numerically favorable characteristics (sparse, local, and parallel), and thus permits an efficient engineering implementation. We show results of the control law tested on an indoor helicopter platform.w tested on an indoor helicopter platform.)
A bootstrappable bio-plausible design for visual pose stabilization + (We consider the problem of purely visual p … We consider the problem of purely visual pose stabilization of a second-order rigid-body system: how to choose forces and torques, based on the visual input alone, such that the view converges to a memorized goal image. Emphasis has been given to the bio-plausibility of the computation, in the sense that the control laws could be in principle implemented on the neural substrate of simple insects. We show that stabilizing laws can be realized by bilinear/quadratic operations on the visual input. Moreover, the control laws can be ``bootstrapped'' (learned unsupervisedly) from experience, which further substantiate the bio-plausibility of such computation. the bio-plausibility of such computation.)
Specifying and Analyzing Networked and Layered Control Systems Operating on Multiple Clocks + (We consider the problem of reasoning about … We consider the problem of reasoning about networked and layered control systems using assume-guarantee specifications. As these systems are formed by the interconnection of components that operate under various clocks, we introduce a new logic, Multiclock Logic (MCL), to be able to express the requirements of components form the point of view of their local clocks. Specifying components locally promotes independent design and component reuse. We carry out a contract-based analysis of a control system implemented via two control algorithms (model predictive control and feedback linearization) running on their own processors and clocks. Then we implement each of the contracts to build a system. The system performs as desired when the requirements derived from our system-level analysis are respected. Violating the constraints required by the contract-based analysis of the system leads to error.sed analysis of the system leads to error.)
Temporal Logic Control of Switched Affine Systems with an Application in Fuel Balancing + (We consider the problem of synthesizing hi … We consider the problem of synthesizing hier- archical controllers for discrete-time switched affine systems subject to exogenous disturbances that guarantee that the trajectories of the system satisfy a high-level specification expressed as a linear temporal logic formula. Our method builds upon recent results on temporal logic planning and embedded controller synthesis. First, the control problem is lifted to a discrete level by constructing a finite transition system that abstracts the behavior of the underlying switched system. At the discrete level, we recast the problem as a two player temporal logic game by treating the environment driven switches as adversaries. The solution strategy for the game (i.e. the discrete plan) is then implemented at the continuous level by solving finite-horizon optimal control problems that establish reachability between discrete states and that compensate the effects of continuous disturbances. We also extend the earlier work by making efficient use of propositions in the temporal logic formula to drive the abstraction procedure and to facilitate the computation of continuous input at implementation time.An aircraft fuel system example is formulated; and solved using the proposed method. This sample problem demonstrates the applicability of the abstraction procedure and correct-by-construction controllers to regulate the fuel levels in multiple tanks during interesting operations like aerial refueling.eresting operations like aerial refueling.)
Distributed Synthesis of Control Protocols for Smart Camera Networks + (We consider the problem of synthesizing co … We consider the problem of synthesizing control protocols for smart camera networks where the goal is to guarantee that certain linear temporal logic (LTL) specifications related to a given surveillance task are met. We first present a centralized control architecture for assigning pan-tilt-zoom (PTZ) cameras to targets so that the specification is met for any admissible behavior of the targets. Then, in order to alleviate the computational complexity associated with LTL synthesis and to enable implementation of local control protocols on individual PTZ cameras, we propose a distributed synthe- sis methodology. The main idea is to decompose the global specification into local specifications for each PTZ camera. A thorough design example is presented to illustrate the steps of the proposed procedure.trate the steps of the proposed procedure.)
Hot-swapping robot task goals in reactive formal synthesis + (We consider the problem of synthesizing ro … We consider the problem of synthesizing robot controllers to realize a task that unpredictably changes with time. Tasks are formally expressed in the GR(1) fragment of temporal logic, in which some of the variables are set by an adversary. The task changes by the addition or removal of goals, which occurs online (i.e., at run-time). We present an algorithm for mending control strategies to realize tasks after the addition of goals, while avoiding global re-synthesis of the strategy. Experiments are presented for a planar surveillance task in which new regions of interest are incrementally added. Run-times are empirically shown to be extremely favorable compared to re-synthesizing from scratch. We also present an algorithm for mending control strategies for the removal of goals. While in this setting the original strategy is still feasible (as we prove), our algorithm provides a more satisfying solution by âtightening loose ends.â Both algorithms are shown to yield so-called reach annotations, and thus the control strategies are easily amenable to other algorithms concerning incremental synthesis, e.g., as in previous work by the authors for robot navigation in uncertain environments.obot navigation in uncertain environments.)
Equilibrium Controllability for a Class of Mechanical Systems + (We define a notion of controllability for … We define a notion of controllability for mechanical systems which determinesthe configurations which are accessible from a given configuration. Wederive sufficient conditions for this notion of controllability in terms ofthe given inputs, their Lie brackets, and their covariant derivatives.brackets, and their covariant derivatives.)
Real Time Trajectory Generation for Differentially Flat Systems with Unstable Zero Dynamics + (We define the real time trajectory generat … We define the real time trajectory generation problem to be how to generate,possibly with some delay, a full state space and input trajectory in realtime from an output trajectory that is given online, while allowing atradeoff between stability and performance. Wepropose two algorithms that solve the real time trajectory generationproblem for flat systems with zero dynamics, and discuss some interestingproperties. We explicitly address the tradeoff between stability andperformance. The algorithms are validated in simulations and experimentswith a thrust vectored ducted fan aircraft.ith a thrust vectored ducted fan aircraft.)
A two-state ribosome and protein model can robustly capture the chemical reaction dynamics of gene expression + (We derive phenomenological models of gene … We derive phenomenological models of gene expression from a mechanistic description of chemical reactions using an automated model reduction method. Using this method, we get analytical descriptions and computational performance guarantees to compare the reduced dynamics with the full models. We develop a new two-state model with the dynamics of the available free ribosomes in the system and the protein concentration. We show that this new two-state model captures the detailed mass-action kinetics of the chemical reaction network under various biologically plausible conditions on model parameters. On comparing the performance of this model with the commonly used mRNA transcript-protein dynamical model for gene expression, we analytically show that the free ribosome and protein model has superior error and robustness performance.superior error and robustness performance.)

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