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Evaluation of Bleed Valve Rate Requirements in Nonlinear Control of Rotating Stall + (In this paper we evaluate the actuator rat … In this paper we evaluate the actuator rate requirements for control of rotating stallusing a bleed valve and provide tools for predicting these requirements. Modification ofboth the stable and unstable parts of the compressor characteristic via addition ofcontinuous air injection serves to reduce the requirement of a bleed valve used for thepurpose of rotating stall stabilization. Analytical tools based on low order models (2-3states) and simulation tools based on a reduced order model (37 states) are described. Ableed actuator rate limit study is presented to compare the actuator requirementspredicted by theory, simulation, and experiment. The comparisons show that the predictionsobtained from theory and simulations share the same trend as the experiments, withincreasing accuracy as the complexity of the underlying model increases. Some insights onthe design of a bleed-compressor pair are given.sign of a bleed-compressor pair are given.)
Delay-Based Approximations of Biological Systems for Analysis and Design + (In this paper we explore the use of time-d … In this paper we explore the use of time-delayed differential equation as a means of obtaining a simplified description of very high order dynamics.This paper finds results for a particular type of system, a single-input single-output (SISO) linear system with a nonlinear feedback. We begin with a high dimensional system in state space and reduce the dimension by finding a delay based approximation which could be a smaller set of integro-differential equations or DDEs. We argue that approximations of high order linear subsystems whose distribution functions have relatively smaller variance such as delta functions, give a conservative approximation of a system's stable parameter space. Through examples inspired by biology, we show how these approximations can be used to verify stability. We analyze the system's stability and robustness dependence on statistical properties, mainly relative variance and expectation for a symmetric distribution function.ion for a symmetric distribution function.)
Differential Flatness and Absolute Equivalence of Nonlinear Control Systems + (In this paper we give a formulation of dif … In this paper we give a formulation of differential flatness---a concept originallyintroduced by Fleiss, Levine, Martin, and Rouchon---in terms of absolute equivalencebetween exterior differential systems. Systems which are differentially flat have severaluseful properties which can be exploited to generate effective control strategies fornonlinear systems. The original definition of flatness was given in the context ofdifferentiable algebra, and required that all mappings be meromorphic functions. Ourformulation of flatness does not require any algebraic structure and allows one to usetools from exterior differential systems to help characterize differentially flat systems.In particular, we shown that in the case of single input control systems (i.e.,codimension 2 Pfaffian systems), a system is differentially flat if and only if it isfeedback linearizable via static state feedback. However, in higher codimensions feedbacklinearizability and flatness are *not* equivalent: one must be careful with the role oftime as well the use of prolongations which may not be realizable as dynamic feedbacks ina control setting. Applications of differential flatness to nonlinear control systems andopen questions will be discussed.tems and open questions will be discussed.)
The Caltech Multi-Vehicle Wireless Testbed + (In this paper we introduce the Caltech Mul … In this paper we introduce the CaltechMulti-Vehicle Wireless Testbed (MVWT), a platform for testingdecentralized control methodologies for multiple vehiclecoordination and formation stabilization. The testbed consists ofeight mobile vehicles, an overhead vision system providingGPS-like position information and wireless Ethernet forcommunications. Each vehicle rests on omni-direction casters andis powered by two high-performance ducted fans. Thus, a uniquefeature of our testbed is that the vehicles have second orderdynamics, requiring real-time feedback algorithms to stabilize thesystem while performing cooperative tasks. The testbed will beused by various research groups at Caltech and elsewhere as ameans to validate theoretical advances in multiple-vehiclecoordination and control, networked control systems, real timenetworking and high confidence distributed computation.d high confidence distributed computation.)
Nonholonomic Motion Planning: Steering Using Sinusoids + (In this paper we investigate methods for s … In this paper we investigate methods for steering systems with nonholonomicconstraints between arbitrary configurations. Early work by Brockett derives the optimalcontrols for a set of canonical systems in which the tangent space to the configurationmanifold is spanned by the input vector fields and their first order Lie brackets. UsingBrockett's result as motivation, we derive suboptimal trajectories for systems which arenot in canonical form and consider systems in which it takes more than one level ofbracketing to achieve controllability. These trajectories use sinusoids at integrallyrelated frequencies to achieve motion at a given bracketing level. We define a class ofsystems which can be steered using sinusoids (chained systems) and give conditions underwhich a class of two-input systems can be converted into this form.t systems can be converted into this form.)
Optimal Control of Affine Connection Control Systems: A Variational Approach + (In this paper we investigate the optimal c … In this paper we investigate the optimal control of affine connectioncontrol systems. The formalism of the affine connection can be used todescribe geometrically the dynamics of me chanical systems, including thosewith nonholonomic constraints. In the standard variational approach to suchproblems, one converts an n dimensional second order system into a 2ndimensional first order system, and uses these equations as constraints onthe optimization. An alternative approach, which we develop in this paper,is to include the system dynamics as second order constraints of theoptimization, and optimize relative to variations in the configurationspace. Using the affine connection, its associated tensors, and the notionof covariant differentiation, we show how variations in the configurationspace induce variations in the tangent space. In this setting, we derivesecond order equations have a geometric formulation parallel to that of thesystem dynamics. They also specialize to results found in the literature.ialize to results found in the literature.)
On Sensor Fusion in the Presence of Packet-Dropping Communication Channels + (In this paper we look at the problem of mu … In this paper we look at the problem of multi-sensor data fusion when data is being communicated over channels that drop packets randomly. We are motivated by the use of wireless links for communication among nodes in upcoming sensor networks. We wish to identify the information that should be communicated by each node to others given that some of the information it had transmitted earlier might have been lost. We solve the problem exactly for the case of two sensors and study the performance of the algorithm when more sensors are present. For the two-sensor case, the performance of our algorithm is optimal in the sense that if a packet is received from the other sensor, it is equivalent to receiving all previous measurements, irrespective of the packet drop pattern. irrespective of the packet drop pattern.)
Nonholonomic control systems: from steering to stabilization with sinuoids + (In this paper we present a control law for … In this paper we present a control law for globally asymptotically stabilizing a classof controllable nonlinear systems without drift. The control law converts into closed loopfeedback earlier strategies for open loop steering of nonholonomic systems using sinusoidsat integrally related frequencies. The global result is obtained by introducing saturationfunctions. Simulation results for stabilizing a simple kinematic model of an automobileare included.matic model of an automobile are included.)
Configuration Controllability of Simple Mechanical Control Systems + (In this paper we present a definition of " … In this paper we present a definition of "configuration controllability" formechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metricminus potential energy. A computable test for this new version of controllability is alsoderived. This condition involves a new object which we call the symmetric product. Ofparticular interest is a definition of "equilibrium controllability" for whichwe are able to derive computable sufficient conditions. Examples illustrate the theory.onditions. Examples illustrate the theory.)
Cone Invariance and Rendezvous of Multiple Agents + (In this paper we present a dynamical syste … In this paper we present a dynamical systems framework for analyzing multi-agent rendezvous problemsand characterize the dynamical behavior of the collective system. Recently, the problem of rendezvous has beenaddressed considerably in the graph theoretic framework, which is strongly based on the communication aspects ofthe problem. The proposed approach is based on set invariance theory and focusses on how to generate feedbackbetween the vehicles, a key part of the rendezvous problem. The rendezvous problem is defined on the positionsof the agents and the dynamics is modeled as linear first order systems. The proposed framework however is notfundamentally limited to linear first order dynamics and can be extended to analyze rendezvous of higher order agents.analyze rendezvous of higher order agents.)
A Framework for Lyapunov Certificates for Multi-Vehicle Rendezvous Problems + (In this paper we present a dynamical syste … In this paper we present a dynamical systems representation for multi-agent rendezvous onthe phase plane. We restrict our attention to two agents, each with scalar dynamics. The problem of rendezvous is cast as a stabilization problem, with a set of constraints on the trajectoriesof the agents, defined on the phase plane. We also describe a method to generate control Lyapunov functions that when used in conjunction with a stabilizing control law, such as Sontag'sformula, make sure that the two-agent system attains rendezvous. The main result of this paperis a Lyapunov-like certificate theorem that describes a set of constraints, which when satisfiedare su±cient to guarantee rendezvous.fied are su±cient to guarantee rendezvous.)
Variational Principles in Constrained Systems: Theory and Experiments + (In this paper we present two methods, the … In this paper we present two methods, the nonholonomic method and the vakonomicmethod, for deriving equations of motion for a mechanical system with constraints. Theresulting equations are compared. Results are also presented from an experiment for amodel system: a ball rolling without sliding on a rotating table. Both sets of equationsof motion for the model system are compared with the experimental results. The effects ofvarious forms of friction are considered in the nonholonomic equations. With appropriatefriction terms, the nonholonomic equations of motion for the model system give reasonableagreement with the experimental observations.eement with the experimental observations.)
New Design Principles for Estimation over Fading Channels in Mobile Sensor Networks + (In this paper we provide new design princi … In this paper we provide new design principlesfor estimation over wireless fading channels in mobile sensornetworks. We show how to optimize receiver and transmitterdesigns to improve estimation performance in the applicationlayer. On the receiver side, we show that the optimum packetdrop mechanism is the one that provides a balance betweeninformation loss and communication noise. On the transmitterside, we show how to optimize and adapt the transmissionrate for performance improvement in the application layer.We further provide stability conditions for different designstrategies. The work confirms that delay-sensitive mobilesensor applications require new design paradigms and applyingthe same design principles of data networks can leadto performance degradation. The work also highlights theimportance of cross-layer feedback and provides alternativedesigns if such feedbacks are not available.signs if such feedbacks are not available.)
Synthesis of Correct-by-Construction Behavior Trees + (In this paper we study the problem of synt … In this paper we study the problem of synthesizing correct-by-construction Behavior Trees (BTs) controlling agents in adversarial environments. The proposed approach combines the modularity and reactivity of BTs with the formal guarantees of Linear Temporal Logic (LTL) methods. Given a set of admissible environment specifications, an agent model in form of a Finite Transition System and the desired task in form of an LTL formula, we synthesize a BT in polynomial time, that is guaranteed to correctly execute the desired task. To illustrate the approach, we present three examples of increasing complexity.t three examples of increasing complexity.)
Proportional Derivative (PD) Control on the Euclidean Group + (In this paper we study the stabilization p … In this paper we study the stabilization problem for control systemsdefined on SE(3), the Euclidean group of rigid--body motions.Assuming one actuator is available for each degree of freedom, weexploit geometric properties of Lie groups (and corresponding Liealgebras) to generalize the classical PD control in a coordinate--freeway. For the SO(3) case, the compactness of the group gives rise to anatural metric structure and to a natural choice of preferred controldirection: an optimal (in the sense of geodesic) solution is given tothe attitude control problem. In the SE(3) case, no natural metric isuniquely defined, so that more freedom is left in the control design.Different formulations of PD feedback can be adopted by extending theSO(3) approach to the whole of SE(3) or by breaking the problem into acontrol problem on SO(3) x R^3. For the simple SE(2) case,simulations are reported to illustrate the behavior of the differentchoices. Finally, we discuss the trajectory tracking problem and showhow to reduce it to a stabilization problem, mimicking the usualapproach in R^n.blem, mimicking the usual approach in R^n.)
Ellipsoidal Cones and Rendezvous of Multiple Agents + (In this paper we use ellipsoidal cones to … In this paper we use ellipsoidal cones to achieverendezvous of multiple agents. Rendezvous of multipleagents is shown to be equivalent to ellipsoidal cone invarianceand a controller synthesis framework is presented.We first demonstrate the methodology on first order LTIsystems and then extend it to rendezvous of mechanicalsystems, that is systems that are force driven.ms, that is systems that are force driven.)
Existence of Cascade Discrete-Continuous State Estimators for Systems on a Partial Order + (In this paper, a cascade discrete-continuo … In this paper, a cascade discrete-continuous state estimator on a partialorder is proposed and its existence investigated. The continuous state estimationerror is bounded by a monotonically nonincreasing function of the discrete stateestimation error, with both the estimation errors converging to zero. This workshows that the lattice approach to estimation is general as the proposed estimatorcan be constructed for any observable and discrete state observable system.The main advantage of using the lattice approach for estimation becomes clearwhen the system has monotone properties that can be exploited in the estimatordesign. In such a case, the computational complexity of the estimator can be drasticallyreduced and tractability can be achieved. Some examples are proposed toillustrate these ideas.es are proposed to illustrate these ideas.)
Engineering Principles of Synthetic Biochemical Oscillators with Negative Cyclic Feedback + (In this paper, we analyze the oscillatory … In this paper, we analyze the oscillatory dynamics of a class of cyclic gene regulatory networks and provide engineering principles for the robust synthesis of biochemical oscillators. We first review the first authorâs previous result that the oscillatory parameter regime of the gene regulatory circuits can be rigorously explored by the local stability analysis of a unique equilibrium. The local stability analysis then leads to the first engineering principle that the circuit components, or genes, should be chosen so that the kinetic profiles of the circuit components are similar to each other. Using a homogeneous oscillator model, we further discuss how to reduce the cell-to-cell variability of the oscillators that is caused by intrinsic noise.llators that is caused by intrinsic noise.)
A Geometric Perspective on Bifurcation Control + (In this paper, we analyze the problem of b … In this paper, we analyze the problem of bifurcation control from a geometric perspective. Our goal is to provide coordinate free, geometric conditions under which control can be used to alter the bifurcation properties of a nonlinear control system. These insights are expected to be useful in understanding the role that magnitude and rate limits play in bifurcation control, as well as giving deeper understanding of the types of control inputs that are required to alter the nonlinear dynamics of bifurcating systems. We also use a model from active control of rotating stall in axial compression systems to illustrate the geometric sufficient conditions of stabilizability.ufficient conditions of stabilizability.)
Approximation of Subnetwork Models using Frequency-Domain Data + (In this paper, we approximate models of in … In this paper, we approximate models of interconnectedsystems that are to be used for decentralized controldesign. The suggested approach is based on approximation ofso-called subnetwork models. A subnetwork model is a modelof the interconnected system, as seen from one specificpositionin the network. The simplification is done by usingweighted model reduction, and several approximationcriteriaare given. A new method for weighted model reduction isused. The method is based on a combination of known techniquesthat use semidefinite programming and frequency-datasamplesof transfer functions. The method is guaranteed to preservestability and does not depend strongly on the order of theoriginal model. This is particularly important for largeinterconnected systems. Two examples are given toillustrate the technique.les are given to illustrate the technique.)
Kalman Filtering Over A Packet-delaying Network: A Probabilistic Approach + (In this paper, we consider Kalman filterin … In this paper, we consider Kalman filtering over a packet-delaying network. Given the probability distribution of the delay, we can completely characterize the filter performance via a probabilistic approach. We assume the estimator maintains a buffer of length D so that at each time k, the estimator is able to retrieve all available data packets up to time k â D + 1. Both the cases of sensor with and without necessary computation capability for filter updates are considered. When the sensor has no computation capability, for a given D, we give lower and upper bounds on the probability for which the estimation error covariance is within a prescribed bound. When the sensor has computation capability, we show that the previously derived lower and upper bounds are equal to each other. An approach for determining the minimum buffer length for a required performance in probability is given and an evaluation on the number of expected filter updates is provided. Examples are provided to demonstrate the theory developed in the paper.nstrate the theory developed in the paper.)
Estimation with Information Loss: Asymptotic Analysis and Error Bounds + (In this paper, we consider a discrete time … In this paper, we consider a discrete time stateestimation problem over a packet-based network. In eachdiscrete time step, the measurement is sent to a Kalmanfilter with some probability that it is received or dropped.Previous pioneering work on Kalman filtering with intermittentobservation losses shows that there exists a certain threshold ofthe packet dropping rate below which the estimator is stable inthe expected sense. In their analysis, they assume that packetsare dropped independently between all time steps. However wegive a completely different point of view. On the one hand, itis not required that the packets are dropped independently butjust that the information gain pi_g, defined to be the limit of theratio of the number of received packets n during N time stepsas N goes to infinity, exists. On the other hand, we show thatfor any given pi_g, as long as pi_g > 0, the estimator is stablealmost surely, i.e. for any given epsilon > 0 the error covariancematrix P{k is bounded by a finite matrix M, with probability1 â epsilon. Given an error tolerance M, pi_g can in turn be found.We also give explicit formula for the relationship between Mand epsilon.mula for the relationship between M and epsilon.)
Robust Control over a Packet-Based Network + (In this paper, we consider a robust networ … In this paper, we consider a robust network control problem. We consider linear unstable and uncertain discrete time plants with a network between the sensors and controller and the controller and plant. We investigate two defining characteristics of network controlled systems and the impact of uncertainty on these. Namely, the minimum data rates required for the two networks and the tolerable data drop out in the form of packet losses. We are able to derive sufficient conditions in terms of the minimum data rate and minimum packet arrival rate to ensure stability of the closed loop system.nsure stability of the closed loop system.)
Towards Robust Control Over a Packet Dropping Network + (In this paper, we consider a robust networ … In this paper, we consider a robust networkcontrol problem. We consider linear unstable and uncertaindiscrete time plants with a network between the sensor andcontroller and the controller and plant. We investigate theeffect of data drop out in the form of packet losses. Fourdistinct control schemes are explored and sufficient conditionsto ensure almost sure stability of the closed loop system arederived for each of them in terms of minimum packet arrivalrate and the maximum uncertainty. arrival rate and the maximum uncertainty.)
Control Over a Packet Dropping Network with Norm Bounded Uncertainties + (In this paper, we consider a robust networ … In this paper, we consider a robust networked control problem. We consider linear unstable and uncertain discrete time plants with a network between the sensor and controller as well as between the controller and plant. We investigate the effect of data drop out in the form of packet losses and we focus on the tradeoff between packet arrival rate versus the uncertainties of the system dynamics. We show that the minimum packet arrival rate and the maximum uncertainty of the system dynamics have a positive correlation. Four distinct control schemes are explored and serve as examples to study this tradeoff. We derive sufficient condition for each scheme to ensure almost sure stability of the closed loop system. Simulation and examples are provided to assist the theory.amples are provided to assist the theory.)

(In this paper, we consider a robust network control problem. We consider)

Effective Sensor Scheduling Schemes in a Sensor Network by Employing Feedback in the Communication Loop + (In this paper, we consider a state estimation problem over a bandwidth limited network. A sensor network consisting of N sensors is used to observe the states of M plants, but only p les N sensors can transmit their measurements to a centralized esti.....)
Data Transmission over Networks for Estimation + (In this paper, we consider the following p … In this paper, we consider the following problem. Suppose a sensor is taking measurements of a dynamic process.It needs to communicate the information over a network of communication links that can drop packets stochastically. Whatis the optimal processing at each node in the network? We provide a strategy that yields the optimal performance at thecost of constant memory and processing at each node. We also provide conditions on the network for the estimate errorcovariance to be stable under this algorithm.ariance to be stable under this algorithm.)
Finite-Horizon Optimal Control and Stabilization of Time-Scalable Systems + (In this paper, we consider the optimal con … In this paper, we consider the optimal control of time-scalable systems.The time-scaling property is shown to convert the PDE associatedwith the Hamilton-Jacobi-Bellman (HJB) equation to a purely spatial PDE. Solution of this PDE yields the value function at a fixed time, and that solution can bescaled to find the value function at any point in time. Furthermore, in certain cases the unscaled control law stabilizes the system, and the unscaled value function acts as aLyapunov function for that system. For the example of the nonholonomic integrator, this PDE is solved, and the resulting optimal trajectories coincide with the known solution to that problem.e with the known solution to that problem.)
On a Decentralized Active Sensing Strategy using Mobile Sensor Platforms in a Network + (In this paper, we consider the problem of … In this paper, we consider the problem of activesensing using mobile sensor nodes that are jointly estimatingthe state of a dynamic target as a sensor network. We proposea gradient search-based decentralized algorithm that demonstratesthe benefits of distributed sensing. We then examine thetask of tracking multiple targets. We use a greedy algorithmfor associating sensors with targets along with the gradientsearchstrategy for sensor vehicle motion planning. Simulationresults show that these simple decentralized strategies performquite well and the sensor nodes exhibit interesting cooperativebehavior. exhibit interesting cooperative behavior.)
The Effect of Sensor Health on State Estimation + (In this paper, we consider the problem of … In this paper, we consider the problem of state estimationusing the standard Kalman filter recursions which takesaccount of the available sensor health information. Givena stochastic description of the sensor health, we are ableto show that the expected error covariance converges to aunique value for all initial values, while the availableprevious work only showed the upper bound of the expectederror covariance converges. Our approach provides boththeoretical value to the analysis as well as the potentialto get tighter upper bound. Our results provide a criterionof evaluating the sensor measurement. In the multisensorfusion problem, depending on the system error tolerancelevels, it can then be determined whether to fuse aparticular sensor measurement or not. Examples andsimulations are provided to assist the theory.lations are provided to assist the theory.)
An Iterative Abstraction Algorithm for Reactive Correct-by-Construction Controller Synthesis + (In this paper, we consider the problem of … In this paper, we consider the problem of synthesizing correct-by-construction controllers for discrete-time dynamical systems. A commonly adopted approach in the literature is to abstract the dynamical system into a finite transition system (FTS) and thus convert the problem into a two player game between the environment and the system on the FTS. The controller design problem can then be solved using synthesis tools for general linear temporal logic or generalized reactivity(1) (GR1) specifications. In this article, we propose a new abstraction algorithm. Instead of generating a single FTS to represent the system, we generate two FTSs, which are underand over-approximations of the original dynamical system. We further develop an iterative abstraction scheme by exploiting the concept of winning sets, i.e., the sets of states for which there exists a winning strategy for the system. Finally, the e�ciency of the new abstraction algorithm is illustrated by numerical examples.ithm is illustrated by numerical examples.)
Sensor Scheduling Algorithms Requiring Limited Computation + (In this paper, we consider the scenario wh … In this paper, we consider the scenario where many sensorsco-operate to estimate a process. Only one sensor can takea measurement at any time step. We wish to come up withoptimal sensor scheduling algorithms. The problem is motivatedby the use of sonar range-finders used by the vehicleson the Caltech Multi-Vehicle Wireless Testbed. We see thatthis problem involves searching a tree in general and proposeand analyze two strategies for pruning the tree to keepthe computation limited. The first is a sliding window strategymotivated by the Viterbi algorithm, and the second oneuses thresholding. We also study a technique that employschoosing the sensors randomly from a probability distributionwhich can then be optimized. The performance of thealgorithms are illustrated with the help of numerical examples.rated with the help of numerical examples.)
Receding Horizon Control for Temporal Logic Specifications + (In this paper, we describe a receding hori … In this paper, we describe a receding horizon scheme that satisfies a class of linear temporal logic specifications sufficient to describe a wide range of properties including safety, stability, progress, obligation, response and guarantee. The resulting embedded control software consists of a goal generator, a tra jectory planner, and a continuous controller. The goal generator essentially reduces the tra jectory generation problem to a sequence of smaller problems of short horizon while preserving the desired system-level temporal properties. Subsequently, in each iteration, the tra jectory planner solves the corresponding short-horizon problem with the currently observed state as the initial state and generates a feasible tra jectory to be implemented by the continuous controller. Based on the simulation property, we show that the composition of the goal generator, tra jectory planner and continuous controller and the corresponding receding horizon scheme guarantee the correctness of the system. To handle failures that may occur due to a mismatch between the actual system and its model, we propose a response mechanism and illustrate, through an example, how the system is capable of responding to certain failures and continues to exhibit a correct behavior.d continues to exhibit a correct behavior.)
An In Silico Modeling Toolbox for Rapid Prototyping of Circuits in a Biomolecular “Breadboard” System + (In this paper, we develop an experimentall … In this paper, we develop an experimentally val- idated MATLAB software toolbox as an accompaniment to an in vitro cell-free biomolecular “breadboard” system. The toolbox gives insight into the dynamics of unmeasured states in the cell-free system, accounting especially for the resource usage. Parameter lumping and the reduced order modeling are used to maintain computational tractability and to avoid ill-conditioning. The toolbox allows for most applications to be implemented with standard set of commands for ease of use. Due to the breadboarding nature of the underlying cell-free sys- tem, the toolbox provides a general framework for experiment planning and predictive modeling for synthetic biomolecular circuits cell-free systems, accelerating our capacity to rationally design circuits from well characterized parts.gn circuits from well characterized parts.)
Trajectory generation for the N-trailer problem using Goursat normal form + (In this paper, we develop the machinery of … In this paper, we develop the machinery of exterior differential forms, more particularly the Goursat normal form for a Pfaffian system, for solving nonholonomic motion planning problems, i.e., motion planning for systems with nonintegrable velocity constraints. We use this technique to solve the problem of steering a mobile robot with n trailers, We present an algorithm for finding a family of transformations which will convert the system of rolling constraints on the wheels of the robot with n trailers into the Goursat canonical form. Two of these transformations are studied in detail. The Goursat normal form for exterior differential systems is dual to the so-called chained-form for vector fields that has been studied previously. Consequently, we are able to give the state feedback law and change of coordinates to convert the N-trailer system into chained form. Three methods for planning trajectories for chained-form systems using sinusoids, piecewise constants, and polynomials as inputs are presented.The motion planning strategy is therefore to first convert the N-trailer system into Goursat form, use this to find the chained-form coordinates, plan a path for the corresponding chained-form system, and then transform the resulting trajectory back into the original coordinates. Simulations and frames of movie animations of the N-trailer system for parallel parking and backing into a loading dock using this strategy are included.ing dock using this strategy are included.)
Consensus problems in networks of agents with switching topology and time-delays + (In this paper, we discuss consensus proble … In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no time-delays, ii) networks with fixed topology and communication time-delays, and iii) max-consensus problems (or leader determination) for groups of discrete-time agents. In each case, we introduce a linear/nonlinear consensus protocol and provide convergence analysis for the proposed distributed algorithm. Moreover, we establish a connection between the Fiedler eigenvalue of the information flow in a network (i.e. algebraic connectivity of the network) and the negotiation speed (or performance) of the corresponding agreement protocol. It turns out that balanced digraphs play an important role in addressing average-consensus problems. We introduce disagreement functions that play the role of Lyapunov functions in convergence analysis of consensus protocols. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results. effectiveness of our theoretical results.)
Resource Competition as a Source of Non-Minimum Phase Behavior in Transcription-Translation Systems + (In this paper, we explore how resource lim … In this paper, we explore how resource limitations can lead to coupling interactions between orthogonal com- ponents in a transcription-translation system and the effect those interactions have on its dynamical behavior. To illustrate these ideas, we present a motivating example featuring a classical network motif: the signal cascade. We show that through coupling interactions arising from competition for limited resources, the system exhibits a non-minimum phase step response. These observations lead us to identify a key network motif with the potential to introduce right half plane zeros into the system transfer function. We characterize the parametric conditions under which the network motif produces a non-minimum phase transfer function and illustrate with two examples how resource limitations can 1) introduce the network motif through these coupling interactions, 2) satisfy the parametric conditions sufficient to produce a right half plane zero.icient to produce a right half plane zero.)
Frequency-Weighted Model Reduction with Applications to Structured Models + (In this paper, we generalize a recently pr … In this paper, we generalize a recently proposedmethod for model reduction of linear systems to the frequencyweightedcase. The method uses convex optimization and can beused both with sample data and exact models. We also derivesimple a priori bounds on the frequency-weighted error. Wecombine the method with a rank-minimization heuristic, toapproximate multi-inputÂmulti-output systems. We also presenttwo applications Â environment compensation and simpli�cationof interconnected models Â where we argue the proposedmethods are useful. we argue the proposed methods are useful.)
Consensus Protocols for Networks of Dynamic Agents + (In this paper, we introduce a consensus pr … In this paper, we introduce a consensus protocol for a network of dynamic agents that allows the agents to reach a decision in a distributed and cooperative fashion. We consider both linear and nonlinear protocols as well as the characteristic function of the communication links in the network. This includes links with delay and (possible) distortion/filtering effects. It turns out that for a number of protocols, the convergence properties and the decision-value obtained via this protocol is strongly related to connectivity and algebraic graph theoretic properties of the information flow in the network of decision-making agents. Standard tools from multivariable control and linear control theory such as Nyquist plots appear naturally for convergence analysis of the obtained linear protocols. For the analysis of the nonlinear protocols, certain disagreement costs are constructed that are minimized by the consensus protocols in a distributed way. Simulation results are provided for attitude alignment of a group of 20 dynamic agents.alignment of a group of 20 dynamic agents.)
Synthesis of Static Test Environments for Observing Sequence-like Behaviors in Autonomous Systems + (In this paper, we investigate formal test- … In this paper, we investigate formal test-case generation for high-level mission objectives, specifically reachability, of autonomous systems. We use Kripke structures to represent the high-level decision-making of the agent under test and the abstraction of the test environment. First, we define the notion of a test specification, focusing on a fragment of linear temporal logic represented by sequence temporal logic formulas. Second, we formulate the problem of test graph synthesis to find a test configuration for which the agent must satisfy the test specification to satisfy its mission objectives. We an algorithm, based on network flows, for synthesizing a test graph by restricting transitions, represented by edge deletions, on the original graph induced by the Kripke structures. The algorithm synthesizes the test graph iteratively using an integer linear program. We prove completeness for our algorithm, and we show that the edge deletions in each iteration maintain feasibility of the integer linear program in the subsequent iteration. We formalize the notion of a minimally constrained test graph in terms of maximum flow, and prove the synthesized test graph to be minimally constrained. We demonstrate our algorithm on a simple graph and on gridworlds.rithm on a simple graph and on gridworlds.)
Pre-orders for Reasoning about Input-to-State Stability Properties of Hybrid Systems + (In this paper, we investigate pre-orders f … In this paper, we investigate pre-orders for reasoning about input-to-state stability properties of hybrid systems. We define the notions of uniformly continuous input simulations and bisimulations, which extend the notions in previous work to include inputs. We show that uniformly con- tinuous input bisimulations preserve incremental input-to-state stability of hybrid systems, and thus provide a basis for constructing abstractions for verification. We show that Lyapunov function based input-to-state stability analysis can be cast in our framework as constructing a simpler one-dimensional system, using a uniformly continuous input simulation, which is input-to-state stable, and thus, inferring the input-to-state stability of the original system.to-state stability of the original system.)
Bisimulations for Reasoning about Input-to-State Stability Properties of Hybrid Systems + (In this paper, we investigate pre-orders f … In this paper, we investigate pre-orders for reason- ing about input-to-state stability properties of hybrid systems. We define the notions of uniformly continuous input simulations and bisimulations, which extend the notions in previous work to include inputs. We show that uniformly continuous input bisimulations preserve incremental input-to-state stability of hybrid systems, and thus provide a basis for constructing abstractions for verification. We show that Lyapunov function based input-to-state stability analysis can be cast in our frame- work as constructing a simpler one-dimensional system, using a uniformly continuous input simulation, which is input-to-state stable, and thus, inferring the input-to-state stability of the original system.to-state stability of the original system.)
Polyhedral Cone Invariance Applied to Rendezvous of Multiple Agents + (In this paper, we pose the N-scalar agent … In this paper, we pose the N-scalar agent rendezvousas a polyhedral cone invariance problem in the Ndimensional phase space. The underlying dynamics of theagents are assumed to be linear. We derive a conditionfor positive invariance for polyhedral cones. Based on thiscondition, we demonstrate that the problem of determining acertificate for rendezvous can be stated as a convex feasibilityproblem. Under certain rendezvous requirements, we showthat there are no robust closed-loop linear solutions that satisfythe invariance conditions. We show that the treatment of therendezvous problem on the phase plane can be extended tothe case where agent dynamics are non-scalar. case where agent dynamics are non-scalar.)
Distributed Cooperative Control of Multiple Vehicle Formations Using Structural Potential Functions + (In this paper, we propose a framework for … In this paper, we propose a framework for formation stabilization ofmultiple autonomous vehicles in a distributed fashion. Each vehicle is assumed tohave simple dynamics, i.e. a double-integrator, with a directed (or an undirected)information ow over the formation graph of the vehicles. Our goal is to finda distributed control law (with an efficient computational cost) for each vehiclethat makes use of limited information regarding the state of other vehicles. Here,the key idea in formation stabilization is the use of natural potential functionsobtained from structural constraints of a desired formation in a way that leads toa collision-free, distributed, and bounded state feedback law for each vehicle.unded state feedback law for each vehicle.)
Voluntary lane-change policy synthesis with reactive control improvisation + (In this paper, we propose reactive control … In this paper, we propose reactive control impro- visation to synthesize voluntary lane-change policy that meets human preferences under given traffic environments. We first train Markov models to describe traffic patterns and the motion of vehicles responding to such patterns using traffic data. The trained parameters are calibrated using control improvisation to ensure the traffic scenario assumptions are satisfied. Based on the traffic pattern, vehicle response models, and Bayesian switching rules, the lane-change environment for an automated vehicle is modeled as a Markov decision process. Based on human lane-change behaviors, we train a voluntary lane- change policy using explicit-duration Markov decision process. Parameters in the lane-change policy are calibrated through reactive control improvisation to allow an automated car to pursue faster speed while maintaining desired frequency of lane-change maneuvers in various traffic environments.maneuvers in various traffic environments.)
Distributed Structural Stabilization and Tracking for Formations of Dynamic Multi-Agents + (In this paper, we provide a theoretical fr … In this paper, we provide a theoretical framework that consists ofgraph theoretical and Lyapunov-based approaches to stability analysis and distributed control of multi-agent formations. This framework relays on the notion of graph rigidity as a means of identifying the shape variables of a formation. Using this approach, we can formally define formations of multiple vehicles and three types of stabilization/tracking problems for dynamic multi-agent systems. We show how these three problems can be addressed mutually independent ofeach other for a formation of two agents. Then, we introduce a procedure called dynamic node augmentation that allows construction of a larger formation with more agents that can be rendered structurally stable in a distributed manner from some initial formation that is structurally stable. We provide two examples of formationsthat can be controlled using this approach, namely, the V-formationand the diamond formation.the V-formation and the diamond formation.)
Agreement Problems in Networks with Directed Graphs and Switching Toplogy + (In this paper, we provide tools for conver … In this paper, we provide tools for convergence andperformance analysis of an agreement protocol for anetwork of integrator agents with directed informationflow. We also analyze algorithmic robustness of thisconsensus protocol for networks with mobile nodes andswitching topology. A connection is established between the Fiedler eigenvalue of the graph Laplacian andthe performance of this agreement protocol. We demon-strate that a class of directed graphs, called balancedgraphs, have a crucial role in solving average-consensusproblems. Based on the properties of balanced graphs,a group disagreement function (i.e. Lyapunov function)is proposed for convergence analysis of this agreementprotocol for networks with directed graphs and switching topology.th directed graphs and switching topology.)
Minimally Constrained Testing for Autonomy with Temporal Logic Specifications + (In this paper, we study automated test gen … In this paper, we study automated test generation for discrete decision-making modules in autonomous systems. First, we consider a subset of Linear Temporal Logic to represent formal requirements on the system and the test environment. The system specification captures requirements for the system under test while the test specification captures basic attributes of the test environment known to the system, and additional structure provided by a test engineer, which is unknown to the system. Second, a game graph representing the high-level interaction between the system and the test environment is constructed from transition systems modeling the system and the test environment. We provide an algorithm that finds the projection of the acceptance conditions of the system and test specifications on the game graph. Finally, to ensure that the system meets the test specification in addition to satisfying the system specification, we present a framework to construct a minimally constrained test. Specifically, we formulate this as a multi-commodity network flows problem, and present two optimizations to solve for the minimally constrained test. We conclude with future directions on applying these algorithms to constrain test environments in self-driving applications.environments in self-driving applications.)
Towards a Packet-Based Control Theory - Part I: Stabilization over a Packet-Based Network + (In this paper, we study the classical prob … In this paper, we study the classical problemof stabilizing a Linear Time Invariant (LTI) system in apacket-based network setting. We assume that the LTI systemis unstable but both controllable and observable. The stateinformation is transmitted to the controller over a packetbasednetwork. We also assume that there is a perfect linkfrom the controller to the plant. We give a set of sufficientconditions under which the system can be stabilized for agiven data rate C. In particular, these conditions can yield anupper bound on the minimum C for which the system canbe stabilized. A recursive encoding-decoding scheme and anassociated control law are proposed to achieve stability forrate exceeding this bound. An optimal bit allocation problemis investigated in which we ask about how to allocate thebits in a single packet for a subsystem of a general LTIsystem such that a minimum upper bound on the data rate isachieved.We then formulate the optimal bit allocation problemas a Linear Matrix Inequality (LMI) optimization problemwhich can be solved efficiently using standard Semi-definiteProgramming (SDP) solvers. Examples and simulations aregiven to demonstrate the results.ions are given to demonstrate the results.)
Connected Cruise Control Design Using Probabilistic Model Checking + (In this paper, we synthesize a robust conn … In this paper, we synthesize a robust connected cruise controller with performance guarantee using probabilis- tic model checking, for a vehicle that receives motion informa- tion from several vehicles ahead through wireless vehicle-to- vehicle communication. We model the car-following dynamics of the preceding vehicles as Markov chains and synthesize the connected cruise controller as a Markov decision process. We show through simulations that such a design is robust against imperfections in communication.st against imperfections in communication.)

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