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This paper examines the long-standing problem of linear quadratic regulation and stabilization for Itô stochastic systems with input delay. This problem remains a primary challenge because the separation principle does not hold for Itô stochastic systems. This paper presents a complete solution to the problem: 1) The (sufficient and necessary) solvability condition of the optimal control and the analytical controller are given based on the modified Riccati differential equation defined herein. 2) The sufficient and necessary stabilization condition in mean square sense is explored. We show that the Itô stochastic system with input delay is stabilized if and only if the modified algebraic Riccati equation developed in this paper has a unique positive-definite solution. The essential obstacle encountered in this paper concerns a Delayed Forward-Backward Stochastic Differential Equation (D-FBSDE), which is mathematical challenging. [ABSTRACT FROM PUBLISHER]

This paper proposes a strategy to estimate the velocity and position of neighbor agents using distance measurements only. Since with agents executing arbitrary motions, instantaneous distance-only measurements cannot provide enough information for our objectives, we postulate that agents engage in a combination of circular motion and linear motion. The proposed estimator can be used to develop control algorithms where only distance measurements are available to each agent. As an example, we show how this estimation method can be used to control the formation shape and secure velocity consensus of the agents in a multi agent system. [ABSTRACT FROM PUBLISHER]

This paper introduces a new multi-agent control problem, called an affine formation control problem, with the objective of asymptotically reaching a configuration that preserves collinearity and ratios of distances with respect to a target configuration. Suppose each agent updates its own state using a weighted sum of its neighbor's relative states with possibly negative weights. Then the affine control problem can be solved for either undirected or directed interaction graphs. It is shown in this paper that an affine formation is stabilizable over an undirected graph if and only if the undirected graph is universally rigid, while an affine formation is stabilizable over a directed graph in the $d$-dimensional space if and only if the directed graph is $(d + 1)$-rooted. Rigorous analysis is provided, mainly relying on Laplacian associated with the interaction graph, which contain both positive and negative weights. [ABSTRACT FROM AUTHOR]

We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic nonlinear observer on Lie groups, for continuous-time systems with discrete observations. One of the main features of invariant observers for left-invariant systems on Lie groups is that the estimation error is autonomous. In this paper we first generalize this result by characterizing the (much broader) class of systems for which this property holds. For those systems, the Lie logarithm of the error turns out to obey a linear differential equation. Then, we leverage this “log-linear” property of the error evolution, to prove for those systems the local stability of the IEKF around any trajectory, under the standard conditions of the linear case. One mobile robotics example and one inertial navigation example illustrate the interest of the approach. Simulations evidence the fact that the EKF is capable of diverging in some challenging situations, where the IEKF with identical tuning keeps converging. [ABSTRACT FROM AUTHOR]

In this paper, we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the cumulative cost as the objective function to be minimized. This framework is axiomatically justified in terms of time-consistency of risk assessments, is amenable to dynamic optimization, and is unifying in the sense that it captures a full range of risk preferences from risk neutral (i.e., expectation) to worst case. Within this framework, we propose and analyze an online risk-sensitive MPC algorithm that is provably stabilizing. Furthermore, by exploiting the dual representation of time-consistent, dynamic risk measures, we cast the computation of the MPC control law as a convex optimization problem amenable to real-time implementation. Simulation results are presented and discussed. [ABSTRACT FROM AUTHOR]

This paper studies the stability for a class of systems with time-varying delay subject to controller failure. It explores under what conditions of controller failure the system is still exponentially stable. The concept of controller failure frequency is introduced. First, the delay system with failed controller is modelled as a class of switched delay systems. Next, based on two lemmas developed in this paper and the piecewise Lyapunov functional method, sufficient conditions are provided to guarantee the exponential stability of the system when controller failure occurs, which is in terms of the solvability of a set of linear matrix inequalities (LMIs). Finally, an example of a networked control system is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper considers the problem of controlling discrete-time linear systems from specifications given as formulas of syntactically co-safe linear temporal logic over linear predicates in the state variables. A systematic procedure is developed for the automatic computation of sets of initial states and feedback controllers such that all the resulting trajectories of the closed-loop system satisfy the given specifications. The procedure is based on the iterative construction and refinement of an automaton that enforces the satisfaction of the formula. Linear programming based approaches are proposed to compute the polytope-to-polytope controllers that label the transitions of the automaton. Extensions to discrete-time piecewise affine systems and specifications given as formulas of full linear temporal logic are included. The algorithms developed in this paper were implemented as a software package that is available for download. Their application and effectiveness are demonstrated for several case studies. [ABSTRACT FROM PUBLISHER]

This paper addresses the problem of exponentially stabilizing periodic orbits in a special class of hybrid models—systems with impulse effects—through control Lyapunov functions. The periodic orbit is assumed to lie in a C^1 submanifold Z that is contained in the zero set of an output function and is invariant under both the continuous and discrete dynamics; the associated restriction dynamics are termed the hybrid zero dynamics. The orbit is furthermore assumed to be exponentially stable within the hybrid zero dynamics. Prior results on the stabilization of such periodic orbits with respect to the full-order dynamics of the system with impulse effects have relied on input-output linearization of the dynamics transverse to the zero dynamics manifold. The principal result of this paper demonstrates that a variant of control Lyapunov functions that enforce rapid exponential convergence to the zero dynamics surface, Z, can be used to achieve exponential stability of the periodic orbit in the full-order dynamics, thereby significantly extending the class of stabilizing controllers. The main result is illustrated on a hybrid model of a bipedal walking robot through simulations and is utilized to experimentally achieve bipedal locomotion via control Lyapunov functions. [ABSTRACT FROM PUBLISHER]

This work deals with the analysis and the design of minimum-time control laws for a class of nonlinear discrete-time dynamical systems characterized by \cal K-continuous transition maps and bounded control inputs. In the paper, it is shown that the reachability properties of the target set, even if not robust positively controllable in one state transition, can be exploited to assess the existence of a robust positively controllable set including the target in its interior. This result allows the formulation of a robustified minimum-time control policy, based on iterated online optimizations and guaranteeing the ultimate boundedness of the state-trajectories in the presence of bounded uncertainties, even if the target set is not robust positively controllable. [ABSTRACT FROM PUBLISHER]

For linear discrete state-space models, under certain conditions, the linear least-mean-squares filter estimate has a convenient recursive predictor/corrector format, aka the Kalman filter. The purpose of this paper is to show that the linear minimum variance distortionless response (MVDR) filter shares exactly the same recursion, except for the initialization which is based on a weighted least-squares estimator. If the MVDR filter is suboptimal in mean-squared error sense, it is an infinite impulse response distortionless filter (a deconvolver) which does not depend on the prior knowledge (first- and second-order statistics) on the initial state. In other words, the MVDR filter can be pre-computed and its behaviour can be assessed in advance independently of the prior knowledge on the initial state. [ABSTRACT FROM AUTHOR]

This paper investigates the weighted-averaging dynamic for unconstrained and constrained consensus problems. Through the use of a suitably defined adjoint dynamic, quadratic Lyapunov comparison functions are constructed to analyze the behavior of weighted-averaging dynamic. As a result, new convergence rate results are obtained that capture the graph structure in a novel way. In particular, the exponential convergence rate is established for unconstrained consensus with the exponent of the order of 1-O(1/(m\log2m)) for special tree-like regular graphs. Also, the exponential convergence rate is established for constrained consensus over time-varying graphs, which nontrivially extends the existing result limited to the static graph case and the use of uniform weight matrices. Our main results are developed for directed graphs that are weakly connected, and we also provide statements regarding the rates in case of joint connectivity. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a self-triggered formulation of model predictive control for continuous-time nonlinear input-affine networked control systems. Our control method specifies not only when to execute control tasks but also provides a way to discretize the optimal control trajectory into several control samples, so that the reduction of communication load will be obtained. Stability analysis under the sample-and-hold implementation is also given, which guarantees that the state converges to a terminal region where the system can be stabilized by a local state feedback controller. Some simulation examples validate our proposed framework. [ABSTRACT FROM PUBLISHER]

Networked systems present some key new challenges in the development of fault-diagnosis architectures. This paper proposes a novel distributed networked fault detection methodology for large-scale interconnected systems. The proposed formulation incorporates a synchronization methodology with a filtering approach in order to reduce the effect of measurement noise and time delays on the fault detection performance. The proposed approach allows the monitoring of multirate systems, where asynchronous and delayed measurements are available. This is achieved through the development of a virtual sensor scheme with a model-based resynchronization algorithm and a delay compensation strategy for distributed fault-diagnostic units. The monitoring architecture exploits an adaptive approximator with learning capabilities for handling uncertainties in the interconnection dynamics. A consensus-based estimator with time-varying weights is introduced, for improving fault detectability in the case of variables shared among more than one subsystem. Furthermore, time-varying threshold functions are designed to prevent false-positive alarms. Analytical fault detectability sufficient conditions are derived, and extensive simulation results are presented to illustrate the effectiveness of the distributed fault detection technique. [ABSTRACT FROM PUBLISHER]

In the recent paper by Hamadeh et al. (2012) an elegant analytic criterion for incremental output feedback passivity (iOFP) of cyclic feedback systems (CFS) has been reported, assuming that the constituent subsystems are incrementally output strictly passive (iOSP). This criterion was used to prove that a network of identical CFS can be synchronized under sufficiently strong linear diffusive coupling. A very important class of CFS consists of biological oscillators, named after Brian Goodwin and describing self-regulated chains of enzymatic reactions, where the product of each reaction catalyzes the next reaction, while the last product inhibits the first reaction in the chain. Goodwin's oscillators are used, in particular, to model the dynamics of genetic circadian pacemakers, hormonal cycles and some metabolic pathways. In this technical note we point out that for Goodwin's oscillators, where the individual reactions have nonlinear (e.g., Mikhaelis-Menten) kinetics, the synchronization criterion, obtained by Hamadeh et al., cannot be directly applied. This criterion relies on the implicit assumption of the solution boundedness, dictated also by the chemical feasibility (the state variables stand for the concentrations of chemicals). Furthermore, to test the synchronization condition one needs to know an explicit bound for a solution, which generally cannot be guaranteed under linear coupling. At the same time, we show that these restrictions can be avoided for a nonlinear synchronization protocol, where the control inputs are “saturated” by a special nonlinear function (belonging to a wide class), which guarantees nonnegativity of the solutions and allows to get explicit ultimate bounds for them. We prove that oscillators synchronize under such a protocol, provided that the couplings are sufficiently strong. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel distributed method to stabilize a set of agents moving in a two dimensional environment to a desired rigid formation. In our approach, each agent computes its control input using the relative positions of a set of formation neighbors but, contrary to most existing works, this information is expressed in the agent's own independent local coordinate frame, without requiring any common reference. The controller is based on the minimization of a Lyapunov function that includes locally computed rotation matrices, which are required due to the absence of a common orientation. Our contribution is that the proposed distributed coordinate-free method achieves global stabilization to a rigid formation with the agents using only partial information of the team, does not require any leader units, and is applicable to both single-integrator or unicycle agents. To guarantee global stability, we require that the network induced by the agent interactions belongs to a certain class of undirected rigid graphs in two dimensions, which we explicitly characterize. The performance of the proposed method is illustrated with numerical simulations. [ABSTRACT FROM AUTHOR]

A geometric homogeneity is introduced for evolution equations in a Banach space. Scalability property of solutions of homogeneous evolution equations is proven. Some qualitative characteristics of stability of trivial solution are also provided. In particular, finite-time stability of homogeneous evolution equations is studied. Theoretical results are illustrated on important classes of partial differential equations. [ABSTRACT FROM PUBLISHER]

Zeno behavior is a dynamic phenomenon unique to hybrid systems in which an infinite number of discrete transitions occurs in a finite amount of time. This behavior commonly arises in mechanical systems undergoing impacts and optimal control problems, but its characterization for general hybrid systems is not completely understood. The goal of this paper is to develop a stability theory for Zeno hybrid systems that parallels classical Lyapunov theory; that is, we present Lyapunov-like sufficient conditions for Zeno behavior obtained by mapping solutions of complex hybrid systems to solutions of simpler Zeno hybrid systems defined on the first quadrant of the plane. These conditions are applied to Lagrangian hybrid systems, which model mechanical systems undergoing impacts, yielding simple sufficient conditions for Zeno behavior. Finally, the results are applied to robotic bipedal walking. [ABSTRACT FROM AUTHOR]

This paper studies the Lagrange stabilization of a class of nonlinear systems whose linear part has a singular system matrix and which have multiple periodic (in state) nonlinearities. Both state and output feedback Lagrange stabilization problems are considered. The paper develops a pseudo H\infty control theory to solve these stabilization problems. In a similar fashion to the Strict Bounded Real Lemma in classic H\infty control theory, a Pseudo Strict Bounded Real Lemma is established for systems with a single unstable pole. Sufficient conditions for the synthesis of state feedback and output feedback controllers are given to ensure that the closed-loop system is pseudo strict bounded real. The pseudo-H\infty control approach is applied to solve state feedback and output feedback Lagrange stabilization problems for nonlinear systems with multiple nonlinearities. An example is given to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of robust H∞ estimation for uncertain systems subject to limited communication capacity. The parameter uncertainty belongs to a given convex polytope and the communication limitations include measurement quantization, signal transmission delay, and data packet dropout, which appear typically in a network environment. The problem of H∞ filter design is first solved for a nominal system subject to the aforementioned information limitations, which is then extended to the uncertain case based on the notion of quadratic stability. To further reduce the overdesign in the quadratic framework, this paper also proposes a parameter-dependent filter design procedure, which is much less conservative than the quadratic approach. The quadratic and parameter-dependent approaches provide alternatives for designing robust H∞ filters with different degrees of conservativeness and computational complexity. Two examples, including a mass-spring system, are utilized to illustrate the design procedures proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the application of the dynamic programming approach to constrained stochastic control problems with expected value constraints is demonstrated. Specifically, two such problems are analyzed using this approach. The problems analyzed are the problem of minimizing a discounted cost infinite horizon expectation objective subject to an identically structured constraint, and the problem of minimizing a discounted cost infinite horizon minimax objective subject to a discounted expectation constraint. Using the dynamic programming approach, optimality equations, which are the chief contribution of this paper, are obtained for these problems. In particular, the dynamic programming operators for problems with expectation constraints differ significantly from those of standard dynamic programming and problems with worst-case constraints. For the discounted cost infinite horizon cases, existence and uniqueness of solutions to the dynamic programming equations are explicitly shown by using the Banach fixed point theorem to show that the corresponding dynamic programming operators are contractions. The theory developed is illustrated by numerically solving the constrained stochastic control dynamic programming equations derived for simple example problems. The example problems are based on a two-state Markov model that represents an error prone system that is to be maintained. [ABSTRACT FROM AUTHOR]

Schur-type methods in [6] and [11] solve the robust pole assignment problem by employing the departure from normality of the closed-loop system matrix as the measure of robustness. They work well generally when all poles to be assigned are simple. However, when some poles are close or even repeated, the eigenvalues of the computed closed-loop system matrix might be inaccurate. In this paper, we present a refined Schur method, which is able to deal with the case when some or all of the poles to be assigned are repeated. More importantly, the refined Schur method can still be applied when place [14] and robpole [28] fail to output a solution when the multiplicity of some repeated poles is greater than the input freedom. [ABSTRACT FROM AUTHOR]

We investigate the optimal estimation problem in lossy networked control systems where the control packets are randomly dropped without acknowledgment to the estimator. Most existing results for this setup are concerned with the design of controller, while the optimal estimation and its performance evaluation have been rarely treated. In this paper, we show that, unlike many other cases such as intermittent observations or TCP-like systems, the system state follows a Gaussian mixture distribution with exponentially increasing terms, which leads to a Gaussian sum filter-based optimal estimation. We develop an auxiliary estimator method to establish necessary and sufficient conditions for the stability of the mean estimation error covariance matrices. It is revealed that the stability is independent of the packet loss rate, and is not affected by the lack of acknowledgment. A suboptimal filtering algorithm with improved computational efficiency is then developed. Numerical examples and simulations are employed to illustrate the theoretical results. [ABSTRACT FROM PUBLISHER]

The paper deals with the design of sampled-data controllers which preserve the stabilizing performance of a continuous-time backstepping control strategy. This is achieved through matching of the control Lyapunov functions evolutions at the sampling instants. The method is developed for systems in strict-feedback form. The results are discussed and compared with similar strategies through simulated examples. [ABSTRACT FROM AUTHOR]

An important tool for proving the safety of dynamical systems is the notion of a barrier certificate. In this paper, we prove that every robustly safe ordinary differential equation has a barrier certificate. Moreover, we show a construction of such a barrier certificate based on a set of states that is reachable in finite time. [ABSTRACT FROM AUTHOR]

This paper presents theoretical guarantees for the stability and performance for the singular value decomposition (SVD) system. The SVD System uses the SVD to reduce the dimension of the control inputs within a feedback loop. This is used to meet the rank 1 input constraint imposed by the row-column structure. The row-column structure reduces the number of inputs required to control $mn$ subsystems to $m + n$. The SVD System provides scalable performance for systems coupled using the row-column structure. The results of this paper are the first analytical results for the SVD System when applied to linear subsystems of arbitrary order. The conclusion of all of this is that using the SVD System allows you to reduce the number of inputs while maintaining as close to the same performance as possible. [ABSTRACT FROM PUBLISHER]

Provides information on a paper which main objective is to solve stabilizing output feedback control problems. Information on the min/max algorithm; Detailed information on numerical implementation and examples; Conclusions reached.

Provides an overview of the technical articles and features presented in this issue. [ABSTRACT FROM PUBLISHER]

The rational covariance extension problem to determine a rational spectral density given a finite number of covariance lags can be seen as a matrix completion problem to construct an infinite-dimensional positive-definite Toeplitz matrix the northwest corner of which is given. The circulant rational covariance extension problem considered in this paper is a modification of this problem to partial stochastic realization of periodic stationary process, which are better represented on the discrete unit circle \BBZ 2N rather than on the discrete real line \BBZ . The corresponding matrix completion problem then amounts to completing a finite-dimensional Toeplitz matrix that is circulant. Another important motivation for this problem is that it provides a natural approximation, involving only computations based on the fast Fourier transform, for the ordinary rational covariance extension problem, potentially leading to an efficient numerical procedure for the latter. The circulant rational covariance extension problem is an inverse problem with infinitely many solutions in general, each corresponding to a bilateral ARMA representation of the underlying periodic process. In this paper, we present a complete smooth parameterization of all solutions and convex optimization procedures for determining them. A procedure to determine which solution that best matches additional data in the form of logarithmic moments is also presented. [ABSTRACT FROM PUBLISHER]

In this paper, we present a polynomial level-set method for advecting a semi-algebraic set for polynomial systems. This method uses the sub-level representation of sets. The problem of flowing these sets under the advection map of a dynamical system is converted to a semi-definite program, which is then used to compute the coefficients of the polynomials. The method presented in this paper does not require either the sets being positively invariant or star-shaped. Hence, the proposed algorithm can describe the behavior of system states both inside and outside the domain of attraction and can also be used to describe more complex shapes of sets. We further address the related problems of constraining the degree of the polynomials. Various numerical examples are presented to show the effectiveness of advection approach. [ABSTRACT FROM AUTHOR]

We investigate the supervisor synthesis problem for centralized partially-observed discrete event systems subject to safety specifications. It is well known that this problem does not have a unique supremal solution in general. Instead, there may be several incomparable locally maximal solutions. One then needs a mechanism to select one locally maximal solution. Our approach in this paper is to consider a lower bound specification on the controlled behavior, in addition to the upper bound for the safety specification. This leads to a generalized supervisory control problem called the range control problem. While the upper bound captures the (prefix-closed) legal behavior, the lower bound captures the (prefix-closed) minimum required behavior. We provide a synthesis algorithm that solves this problem by effectively constructing a maximally-permissive safe supervisor that contains the required lower bound behavior. This is the first algorithm with such properties, as previous works solve either the maximally-permissive safety problem (with no lower bound), or the lower bound containment problem (without maximal permissiveness). [ABSTRACT FROM AUTHOR]

In this paper, a new impulsive delay inequality that involves unbounded and nondifferentiable time-varying delay is presented. As an application, some sufficient conditions ensuring stability and stabilization of impulsive systems with unbounded time-varying delay are derived. Some numerical examples are given to illustrate the results. Especially, a stabilizing memoryless controller for a second-order time-varying system with unbounded time-varying delay is proposed. [ABSTRACT FROM AUTHOR]

In the existing control problems for the leader–follower multiagent systems, the leader's dynamics are independent of the followers. In this paper, we consider a tracking control problem for an interconnected leader–follower multiagent system, where the leader's dynamics are interconnected with the states of the followers. It is shown that such a problem can be used to model the autonomous power sharing problem of grid-connected microgrids. In order to solve this problem, a distributed control law using only local information is synthesized. Simulation results are provided to show the effectiveness of the proposed control law. [ABSTRACT FROM PUBLISHER]

The paper deals with the problem of robust output regulation for minimum-phase nonlinear systems in a semiglobal setting. We present a different perspective to the problem of adaptive regulation in which prediction error identification methods, which are routinely used in other control contexts, can be adopted to design robust nonlinear regulators. The proposed control structure combines continuous-time dynamics and “hybrid identifiers”, the latter specifically designed to estimate the actual steady-state control law. The proposed framework encompasses existing frameworks proposed so far in the nonlinear continuous-time literature. [ABSTRACT FROM PUBLISHER]

We present an abstraction and refinement methodology for the automated controller synthesis to enforce general predefined specifications. The designed controllers require quantized (or symbolic) state information only and can be interfaced with the system via a static quantizer. Both features are particularly important with regard to any practical implementation of the designed controllers and, as we prove, are characterized by the existence of a feedback refinement relation between plant and abstraction. Feedback refinement relations are a novel concept introduced in this paper. Our work builds on a general notion of system with set-valued dynamics and possibly non-deterministic quantizers to permit the synthesis of controllers that robustly, and provably, enforce the specification in the presence of various types of uncertainties and disturbances. We identify a class of abstractions that is canonical in a well-defined sense, and provide a method to efficiently compute canonical abstractions. We demonstrate the practicality of our approach on two examples. [ABSTRACT FROM AUTHOR]

This paper addresses the output feedback stabilization problem for discrete-time networked control systems with imperfect input channels, i.e., the controller-actuator channels, where both quantization error and packet dropout are involved. A stabilizability condition is first derived for the single-input-single-output (SISO) case. It is shown that stabilization over quantized lossy channel actually involves a trade-off between robust stability control and robust performance control. Furthermore, the results are expanded to triangularly decoupled multiple-input-multiple-output (MIMO) systems and a necessary and sufficient condition is deduced, which also exhibits a compromise between robust stability control and robust performance control in the individual channel as echoing the SISO case. [ABSTRACT FROM PUBLISHER]

In many practical distributed parameter systems (DPSs), the states of the systems are required to track a desired trajectory repeatedly over a finite duration. It is hard to design the controllers for the systems to obtain uniformity and repetitiveness of the states simultaneously. In this paper, iterative learning control (ILC) based on the eigenspectrum of the system is proposed for a class of parabolic DPS to tackle this control problem. First, Galerkin’s method with the eigenspectrum as the base is applied to the original system to obtain a reduced-order model which exhibits the dominant dynamics of the system. Then, an ILC controller based on the reduced-order model is developed. The stability and convergence of the proposed approach are analyzed and guaranteed under the framework of functional analysis. Finally, simulations on the temperature profile control of a rapid thermal processing system are performed to demonstrate the effectiveness of the developed ILC scheme. [ABSTRACT FROM PUBLISHER]

Average consensus is a widely used algorithm for distributed computing and control, where all the agents in the network constantly communicate and update their states in order to achieve an agreement. This approach could result in an undesirable disclosure of information on the initial state of an agent to the other agents. In this paper, we propose a privacy preserving average consensus algorithm to guarantee the privacy of the initial state and asymptotic consensus on the exact average of the initial values, by adding and subtracting random noises to the consensus process. We characterize the mean square convergence rate of our consensus algorithm and derive the covariance matrix of the maximum likelihood estimate on the initial state. Moreover, we prove that our proposed algorithm is optimal in the sense that it does not disclose any information more than necessary to achieve the average consensus. A numerical example is provided to illustrate the effectiveness of the proposed design. [ABSTRACT FROM PUBLISHER]

This paper is motivated by the desire to develop optimal defensive control strategies that discourage an attacker from engaging in attack while simultaneously encouraging retreat. We develop a general, two-player, differential game in which one player represents an attacker and the opposing player represents the defender. The attacker possesses superior dynamics such that it is capable of terminating the game either in engagement or retreat as it so chooses. The defender is incapable of directly preventing engagement. Instead, the defender uses the manipulation of the attacker’s utility function as a form of indirect control in an attempt to make retreat a more attractive option over engagement. The solution to the overall engage or retreat differential game is found by solving two related optimization problems: the differential game of engagement and the optimal constrained retreat. The equilibrium open-loop control strategies and resulting game values of the attack or retreat game are expressed in terms of the solutions to these subproblems. Within the optimal constrained retreat problem, a value function constraint is imposed in order to prevent the attacker from moving into regions where engagement becomes optimal. This leads to regions of constrained retreat which we refer to as escort regions. [ABSTRACT FROM PUBLISHER]

Natural systems are inextricably affected by noise. Within recent decades, the manner in which noise affects the collective behavior of self-organized systems, specifically, has garnered considerable interest from researchers and developers in various fields. To describe the collective motion of multiple interacting particles, Vicsek et al. proposed a well-known self-propelled particle (SPP) system, which exhibits a second-order phase transition from disordered to ordered motion in simulation; due to its non-equilibrium, randomness, and strong coupling nonlinear dynamics, however, there has been no rigorous analysis of such a system to date. To decouple systems consisting of deterministic laws and randomness, we propose a general method which transfers the analysis of these systems to the design of cooperative control algorithms. In this study, we rigorously analyzed the original Vicsek model under both open and periodic boundary conditions for the first time, and developed extensions to heterogeneous SPP systems (including leader-follower models) using the proposed method. Theoretical results show that SPP systems switch an infinite number of times between ordered and disordered states for any noise intensity and population density, which implies that the phase transition indeed takes a nontraditional form. We also investigated the robust consensus and connectivity of these systems. Moreover, the findings presented in this paper suggest that our method can be used to predict possible configurations during the evolution of complex systems, including turn, vortex, bifurcation, and flock merger phenomena as they appear in SPP systems. [ABSTRACT FROM PUBLISHER]

In this paper, we consider a class of noncooperative $N$- player finite-horizon linear-quadratic dynamic games with linear constraints. We introduce a constrained feedback information structure and provide necessary and sufficient conditions for the existence of a constrained feedback Nash equilibrium. For this class of games we show that the constrained feedback Nash equilibrium can be obtained from a feedback Nash equilibrium associated with an unconstrained multi-parametric linear-quadratic game where the parameters satisfy an equilibrium property. We show that this relation leads to a fixed-point interpretation. Further, under a few additional assumptions, we show that these fixed points can be obtained as solutions of a single large-scale linear-complementarity problem, thereby providing a method to compute the constrained feedback Nash equilibria. We illustrate our results with a numerical example. [ABSTRACT FROM PUBLISHER]

This paper proposes a new iterative solution method for nonlinear stochastic optimal control problems based on path integral analysis. First, we provide an iteration law for solving a stochastic Hamilton-Jacobi-Bellman (SHJB) equation associated to this problem, which is a nonlinear partial differential equation (PDE) of second order. Each iteration procedure of the proposed method is represented by a Cauchy problem for a linear parabolic PDE, and its explicit solution is given by the Feynman-Kac formula. Second, we derive a suboptimal feedback controller at each iteration by using the path integral analysis. Third, the convergence property of the proposed method is investigated. Here, some conditions are provided so that the sequence of solutions for the proposed iteration converges, and the SHJB equation is satisfied. Finally, numerical simulations demonstrate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

The convergence properties of popular nonlinear attitude estimators can be traced to the choice of an attitude error function. This paper considers a nonlinear deterministic direction cosine matrix estimator whose form is derived from an alternate attitude error function. While the resulting estimator shares several properties with those previously presented in the literature, the careful selection of an attitude error function results in an estimator with superior convergence properties. The attitude estimate is propagated using a rate gyroscope measurement and corrected using two or more vector measurements. Simulation and experimental results are presented that highlight the desirable properties of the proposed estimator. [ABSTRACT FROM PUBLISHER]

The problem of secure state estimation and attack detection in cyber-physical systems is considered in this paper. A stochastic modeling framework is first introduced, based on which the attacked system is modeled as a finite-state hidden Markov model with switching transition probability matrices controlled by a Markov decision process. Based on this framework, a joint state and attack estimation problem is formulated and solved. Utilizing the change of probability measure approach, we show that an unnormalized joint state and attack distribution conditioned on the sensor measurement information evolves in a linear recursive form, based on which the optimal estimates can be further calculated by evaluating the normalized marginal conditional distributions. The estimation results are further applied to secure estimation of stable linear Gaussian systems, and extensions to more general systems are also discussed. The effectiveness of the results are illustrated by numerical examples and comparative simulation. [ABSTRACT FROM PUBLISHER]

Feasibility determination has emerged as a widely applied problem in simulation optimization. It seeks to provide all the feasible designs from a finite set of design alternatives based on which the final decision can be chosen by the decision maker. In this paper, we consider the feasibility determination problem in presence of multiple performance measure constraints. The optimal solution to maximize the probability of correct feasibility determination is derived under asymptotic approximation. A corresponding sequential selection procedure is designed for implementation. The numerical testing shows that our approach can enhance the simulation efficiency significantly. [ABSTRACT FROM PUBLISHER]

In this paper, an explicit nonlinear model predictive controller (ENMPC) for the stabilization of nonlinear systems is investigated. The proposed ENMPC is constructed using tensored polynomial basis functions and samples drawn from low-discrepancy sequences. Solutions of a finite-horizon optimal control problem at the sampled nodes are used 1) to learn an inner and outer approximation of the feasible region of the ENMPC using support vector machines, and 2) to construct the ENMPC control surface on the computed feasible region using regression or sparse-grid interpolation, depending on the shape of the feasible region. The attractiveness of the proposed control scheme lies in its tractability to higher-dimensional systems with feasibility and stability guarantees, significantly small online computation times, and ease of implementation. [ABSTRACT FROM PUBLISHER]

This paper considers simulation-based optimization of the performance of a regime-switching stochastic system over a finite set of feasible configurations. Inspired by the stochastic fictitious play learning rules in game theory, we propose an adaptive random search algorithm that uses a smooth best-response sampling strategy and tracks the set of global optima, yet distributes the search so that most of the effort is spent on simulating the system performance at the global optima. The algorithm responds properly to the random unpredictable jumps of the global optimum even when the observations data are temporally correlated as long as a weak law of large numbers holds. Numerical examples show that the proposed scheme yields faster convergence and superior efficiency for finite sample lengths compared with several existing random search and pure exploration methods in the literature. [ABSTRACT FROM PUBLISHER]

The use of multivalued controls derived from a special maximally monotone operator are studied in this paper. Starting with a strongly passive linear system (with possible parametric uncertainty and external disturbances) a multivalued control law is derived, ensuring regulation of the output to a desired value. The methodology used falls in a passivity-based control context, where we study how the multivalued control affects the dissipation equation of the closed-loop system, from which we derive its robustness properties. Finally, some numerical examples together with implementation issues are presented to support the main result. [ABSTRACT FROM PUBLISHER]

Many resource allocation problems can be formulated as an optimization problem whose constraints contain sensitive information about participating users. This paper concerns a class of resource allocation problems whose objective function depends on the aggregate allocation (i.e., the sum of individual allocations); in particular, we investigate distributed algorithmic solutions that preserve the privacy of participating users. Without privacy considerations, existing distributed algorithms normally consist of a central entity computing and broadcasting certain public coordination signals to participating users. However, the coordination signals often depend on user information, so that an adversary who has access to the coordination signals can potentially decode information on individual users and put user privacy at risk. We present a distributed optimization algorithm that preserves differential privacy, which is a strong notion that guarantees user privacy regardless of any auxiliary information an adversary may have. The algorithm achieves privacy by perturbing the public signals with additive noise, whose magnitude is determined by the sensitivity of the projection operation onto user-specified constraints. By viewing the differentially private algorithm as an implementation of stochastic gradient descent, we are able to derive a bound for the suboptimality of the algorithm. We illustrate the implementation of our algorithm via a case study of electric vehicle charging. Specifically, we derive the sensitivity and present numerical simulations for the algorithm. Through numerical simulations, we are able to investigate various aspects of the algorithm when being used in practice, including the choice of step size, number of iterations, and the trade-off between privacy level and suboptimality. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the synchronization control problem for uncertain high-order nonlinear multi-agent systems in a leader-follower scheme, under a directed communication protocol. A robust decentralized control law of minimal complexity is proposed that achieves prescribed, arbitrarily fast and accurate synchronization of the following agents with the leader. The control protocol is decentralized in the sense that the control signal of each agent is calculated based solely on local relative state information from its neighborhood set. Additionally, no information regarding the agents' dynamic model is employed in the design procedure. Moreover, provided that the communication graph is connected and contrary to the related works on multi-agent systems, the controller-imposed transient and steady state performance bounds are fully decoupled from: 1) the underlying graph topology, 2) the control gains selection, and 3) the agents' model uncertainties, and are solely prescribed by certain designer-specified performance functions. Extensive simulation results clarify and verify the approach. [ABSTRACT FROM PUBLISHER]

This paper presents a model reduction method for the class of linear quantum stochastic systems often encountered in quantum optics and related fields. The approach is proposed on the basis of an interpolatory projection ensuring that specific input-output responses of the original and the reduced-order systems are matched at multiple selected points (or frequencies). Importantly, the physical realizability property of the original quantum system imposed by the laws of quantum mechanics is preserved under our tangential interpolatory projection. Error bounds are established for the proposed model reduction method and an avenue to select interpolation points is proposed. A passivity preserving model reduction method is also presented. Examples of both active and passive systems are provided to illustrate the merits of our proposed approach. [ABSTRACT FROM PUBLISHER]