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Showing papers in "IEEE Transactions on Automatic Control in 2017"


Journal ArticleDOI
TL;DR: This paper develops a methodology that allows safety conditions—expression as control barrier functions—to be unified with performance objectives—expressed as control Lyapunov functions—in the context of real-time optimization-based controllers.
Abstract: Safety critical systems involve the tight coupling between potentially conflicting control objectives and safety constraints. As a means of creating a formal framework for controlling systems of this form, and with a view toward automotive applications, this paper develops a methodology that allows safety conditions—expressed as control barrier functions —to be unified with performance objectives—expressed as control Lyapunov functions—in the context of real-time optimization-based controllers. Safety conditions are specified in terms of forward invariance of a set, and are verified via two novel generalizations of barrier functions; in each case, the existence of a barrier function satisfying Lyapunov-like conditions implies forward invariance of the set, and the relationship between these two classes of barrier functions is characterized. In addition, each of these formulations yields a notion of control barrier function (CBF), providing inequality constraints in the control input that, when satisfied, again imply forward invariance of the set. Through these constructions, CBFs can naturally be unified with control Lyapunov functions (CLFs) in the context of a quadratic program (QP); this allows for the achievement of control objectives (represented by CLFs) subject to conditions on the admissible states of the system (represented by CBFs). The mediation of safety and performance through a QP is demonstrated on adaptive cruise control and lane keeping, two automotive control problems that present both safety and performance considerations coupled with actuator bounds.

992 citations


Journal ArticleDOI
TL;DR: It is shown that the proposed control schemes guarantee that all the closed-loop signals are globally bounded and the tracking/stabilization error exponentially converges towards a compact set which is adjustable.
Abstract: In this technical note, the problem of event-trigger based adaptive control for a class of uncertain nonlinear systems is considered. The nonlinearities of the system are not required to be globally Lipschitz. Since the system contains unknown parameters, it is a difficult task to check the assumption of the input-to-state stability (ISS) with respect to the measurement errors, which is required in most existing literature. To solve this problem, we design both the adaptive controller and the triggering event at the same time such that the ISS assumption is no longer needed. In addition to presenting new design methodologies based on the fixed threshold strategy and relative threshold strategy, we also propose a new strategy named the switching threshold strategy. It is shown that the proposed control schemes guarantee that all the closed-loop signals are globally bounded and the tracking/stabilization error exponentially converges towards a compact set which is adjustable.

804 citations


Journal ArticleDOI
TL;DR: The design of asynchronous controller, which covers the well-known mode-independent controller and synchronous controller as special cases, is addressed and the DC motor device is applied to demonstrate the practicability of the derived asynchronous synthesis scheme.
Abstract: The issue of asynchronous passive control is addressed for Markov jump systems in this technical note. The asynchronization phenomenon appears between the system modes and controller modes, which is described by a hidden Markov model. Accordingly, a hidden Markov jump model is used to name the resultant closed-loop system. By utilizing the matrix inequality technique, three equivalent sufficient conditions are obtained, which can guarantee the hidden Markov jump systems to be stochastically passive. Based on the established conditions, the design of asynchronous controller, which covers the well-known mode-independent controller and synchronous controller as special cases, is addressed. The DC motor device is applied to demonstrate the practicability of the derived asynchronous synthesis scheme.

413 citations


Journal ArticleDOI
TL;DR: It is shown that time delays in impulse term may contribute to the stabilization of delay systems, and an impulsive delay inequality is proposed which applies to the delay systems which may be originally unstable, and derive some delay-dependent impulsive control criteria to ensure the stabilize of the addressed systems.
Abstract: The stabilization problem of delay systems is studied under the delay-dependent impulsive control. The main contributions of this technical note are that, for one thing, it shows that time delays in impulse term may contribute to the stabilization of delay systems, that is, a control strategy which does not work without delay feedback in impulse term can be activated to stabilize some unstable delay systems if there exist some time delay feedbacks; for another, it shows the robustness of impulsive control, that is, the designed control strategy admits the existence of some time delays in impulse term which may do harm to the stabilization. In this technical note, from impulsive control point of view we firstly propose an impulsive delay inequality. Then we apply it to the delay systems which may be originally unstable, and derive some delay-dependent impulsive control criteria to ensure the stabilization of the addressed systems. The effectiveness of the proposed strategy is evidenced by two illustrative examples.

411 citations


Journal ArticleDOI
TL;DR: A novel event-triggered control (ETC) strategy for a class of nonlinear feedback systems is proposed that can simultaneously guarantee a finite Lp-gain and a strictly positive lower bound on the inter-event times.
Abstract: Networked control systems are often subject to limited communication resources. By only communicating output measurements when needed, event-triggered control is an adequate method to reduce the usage of communication resources while retaining desired closed-loop performance. In this work, a novel event-triggered control (ETC) strategy for a class of nonlinear feedback systems is proposed that can simultaneously guarantee a finite $\mathcal{L}_{p}$ - gain and a strictly positive lower bound on the inter-event times. The new ETC scheme can be synthesized in an output-based and/or decentralized form, takes the specific medium access protocols into account, and is robust to (variable) transmission delays by design. Interestingly, in contrast with the majority of existing event-generators that only use static conditions, the newly proposed event-triggering conditions are based on dynamic elements, which has several advantages including larger average inter-event times. The developed theory leads to families of event-triggered controllers that correspond to different tradeoffs between (minimum and average) inter-event times, maximum allowable delays and $\mathcal{L}_{p}$ - gains. A linear and a nonlinear numerical example will illustrate all the benefits of this new dynamic ETC scheme.

396 citations


Journal ArticleDOI
TL;DR: Numerical simulations are provided to demonstrate the effectiveness of the theoretical results and the obtained results can be applied to deal with time-varying formation tracking problems, target enclosing problems, and consensus tracking problems for linear multiagent systems with one or multiple targets/leaders.
Abstract: Time-varying formation tracking problems for linear multiagent systems with multiple leaders are studied, where the states of followers form a predefined time-varying formation while tracking the convex combination of the states of multiple leaders. Followers are classified into well-informed ones and uninformed ones, where the neighbor set of the former contains all the leaders, whereas the latter contains no leaders. A formation tracking protocol is constructed using only neighboring relative information. Necessary and sufficient conditions for multiagent systems with multiple leaders to achieve time-varying formation tracking are proposed by utilizing the properties of the Laplacian matrix, where the formation tracking feasibility constraints are also given. An approach to design the formation tracking protocol is presented by solving an algebraic Riccati equation. The obtained results can be applied to deal with time-varying formation tracking problems, target enclosing problems, and consensus tracking problems for linear multiagent systems with one or multiple targets/leaders. Numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

381 citations


Journal ArticleDOI
TL;DR: This technical note is concerned with the design problem of adaptive sliding-mode stabilization for Markov jump nonlinear systems with actuator faults and the main attention focuses on designing the adaptive slide-mode controller to overcome these problems.
Abstract: This technical note is concerned with the design problem of adaptive sliding-mode stabilization for Markov jump nonlinear systems with actuator faults. The specific information including bounds of actuator faults, bounds of the nonlinear term and the external disturbance is not available for the controller design. The main attention focuses on designing the adaptive sliding-mode controller to overcome these problems. Firstly, a sliding-mode surface is constructed such that the reduced-order equivalent sliding motion is stochastically stable. Secondly, the adaptive sliding-mode controller can drive the state trajectories of the system onto the sliding-mode surface in finite time, and can estimate the loss of effectiveness of actuator faults and bounds of the nonlinear term and the external disturbance online. Thirdly, the stochastic stability of the closed-loop system can be guaranteed. Finally, a practical example is provided to demonstrate the effectiveness of the presented results.

344 citations


Journal ArticleDOI
TL;DR: New stability conditions are established for systems with a designed switching strategy where fast switching and slow switching are respectively applied to unstable and stable subsystems, via choosing multiple discontinuous Lyapunov functions in the quadratic form.
Abstract: In this technical note, the problem of stability for a class of slowly switched systems is investigated. By developing a novel multiple discontinuous Lyapunov function approach and exploring the feature of mode-dependent dwell time switching, new stability conditions are established for systems with a designed switching strategy where fast switching and slow switching are respectively applied to unstable and stable subsystems. In particular, stability conditions for linear switched systems are also given via choosing multiple discontinuous Lyapunov functions in the quadratic form. Moreover, stability criteria for the systems consisting of stable subsystems are also derived. It is shown that our proposed results cover some existing ones in literature as special cases, and provide tighter bounds on the dwell time. Finally, some simulation results are provided to show the advantages of the theoretic results obtained.

296 citations


Journal ArticleDOI
TL;DR: In this article, the authors analyzed 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.
Abstract: 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.

292 citations


Journal ArticleDOI
TL;DR: This paper proposes a new Lyapunov function, which is continuous and does not include any sign function, and hence, the chattering phenomenon in most of the existing results is overcome and an optimal algorithm is proposed for the estimation of the settling time.
Abstract: Dealing with impulsive effects is one of the most challenging problems in the field of fixed-time control. In this paper, we solve this challenging problem by considering fixed-time synchronization of complex networks (CNs) with impulsive effects. By designing a new Lyapunov function and constructing comparison systems, a sufficient condition formulated by matrix inequalities is given to ensure that all the dynamical subsystems in the CNs are synchronized with an isolated system in a settling time, which is independent of the initial values of both the CNs and the isolated system. Then, by partitioning impulse interval and using the convex combination technique, sufficient conditions in terms of linear matrix inequalities are provided. Our synchronization criteria unify synchronizing and desynchronizing impulses. Compared with the existing controllers for fixed-time and finite-time techniques, the designed controller is continuous and does not include any sign function, and hence, the chattering phenomenon in most of the existing results is overcome. An optimal algorithm is proposed for the estimation of the settling time. Numerical examples are given to show the effectiveness of our new results.

287 citations


Journal ArticleDOI
TL;DR: A distributed optimization problem with general differentiable convex objective functions is studied for continuous-time multi-agent systems with single-integrator dynamics and it is shown that all agents reach a consensus in finite time while minimizing the team objective function asymptotically.
Abstract: In this paper, a distributed optimization problem with general differentiable convex objective functions is studied for continuous-time multi-agent systems with single-integrator dynamics. The objective is for multiple agents to cooperatively optimize a team objective function formed by a sum of local objective functions with only local interaction and information while explicitly taking into account nonuniform gradient gains, finite-time convergence, and a common convex constraint set. First, a distributed nonsmooth algorithm is introduced for a special class of convex objective functions that have a quadratic-like form. It is shown that all agents reach a consensus in finite time while minimizing the team objective function asymptotically. Second, a distributed algorithm is presented for general differentiable convex objective functions, in which the interaction gains of each agent can be self-adjusted based on local states. A corresponding condition is then given to guarantee that all agents reach a consensus in finite time while minimizing the team objective function asymptotically. Third, a distributed optimization algorithm with state-dependent gradient gains is given for general differentiable convex objective functions. It is shown that the distributed continuous-time optimization problem can be solved even though the gradient gains are not identical. Fourth, a distributed tracking algorithm combined with a distributed estimation algorithm is given for general differentiable convex objective functions. It is shown that all agents reach a consensus while minimizing the team objective function in finite time. Fifth, as an extension of the previous results, a distributed constrained optimization algorithm with nonuniform gradient gains and a distributed constrained finite-time optimization algorithm are given. It is shown that both algorithms can be used to solve a distributed continuous-time optimization problem with a common convex constraint set. Numerical examples are included to illustrate the obtained theoretical results.

Journal ArticleDOI
TL;DR: An adaptive controller is developed that guarantees uniform ultimate boundedness of the closed-loop dynamical system in the face of adversarial sensor and actuator attacks that are time-varying and partial asymptotic stability when the sensors and actuators attacks areTime-invariant.
Abstract: Recent technological advances in communications and computation have spurred a broad interest in control law architectures involving the monitoring, coordination, integration, and operation of sensing, computing, and communication components that tightly interact with the physical processes that they control. These systems are known as cyber-physical systems and due to their use of open computation and communication platform architectures, controlled cyber-physical systems are vulnerable to adversarial attacks. In this technical note, we propose a novel adaptive control architecture for addressing security and safety in cyber-physical systems. Specifically, we develop an adaptive controller that guarantees uniform ultimate boundedness of the closed-loop dynamical system in the face of adversarial sensor and actuator attacks that are time-varying and partial asymptotic stability when the sensor and actuator attacks are time-invariant. Finally, we provide a numerical example to illustrate the efficacy of the proposed adaptive control architecture.

Journal ArticleDOI
TL;DR: A new procedure to design parameter estimators with enhanced performance is proposed, which yields a new parameter estimator whose convergence is established without the usual requirement of regressor persistency of excitation.
Abstract: A new procedure to design parameter estimators with enhanced performance is proposed in the technical note. For classical linear regression forms, it yields a new parameter estimator whose convergence is established without the usual requirement of regressor persistency of excitation. The technique is also applied to nonlinear regressions with “partially” monotonic parameter dependence—giving rise again to estimators with enhanced performance. Simulation results illustrate the advantages of the proposed procedure in both scenarios.

Journal ArticleDOI
TL;DR: A low-complexity state feedback fault-tolerant control scheme guaranteeing prescribed tracking performance is proposed for a family of uncertain nonlinear systems with unknown control directions, in spite of actuation faults, component faults, and unknown nonlinearities.
Abstract: A low-complexity state feedback fault-tolerant control scheme guaranteeing prescribed tracking performance is proposed for a family of uncertain nonlinear systems with unknown control directions. Contrary to the current state-of-the-art, novel error transformation functions and new update laws related to performance functions are introduced to the control design such that no compensators or approximation structures are needed, in spite of actuation faults, component faults, and unknown nonlinearities. The proposed method is verified via a simulation on an inverted pendulum.

Journal ArticleDOI
TL;DR: The dynamic event-triggered control approach is proposed and the stochastic stability of the resulting closed-loop system is proved, and a new dynamic self-triggering mechanism is developed and the additional internal dynamic variable is designed according to the predicted value of the system state and error.
Abstract: In this paper, the event-based control problems for nonlinear stochastic systems are investigated. First, a novel condition for stochastic input-to-state stability is established. Then, the dynamic event-triggered control approach is proposed and the stochastic stability of the resulting closed-loop system is also proved. Next, a new dynamic self-triggering mechanism is developed and the additional internal dynamic variable is designed according to the predicted value of the system state and error, which ensures that the closed-loop system is stochastically stable. It is shown that the lower bounds of interexecution times by the proposed dynamic event-triggered and self-triggered control approaches are all larger than zero, and the so-called Zeno phenomenon is avoided. Compared with the static event-triggering and self-triggering results, the interexecution times by the proposed dynamic approaches are prolonged on the whole. Two simulation examples are provided to show the efficiency of the proposed approaches.

Journal ArticleDOI
TL;DR: A new impulsive delay inequality that involves unbounded and nondifferentiable time-varying delay is presented and some sufficient conditions ensuring stability and stabilization of impulsive systems with unbounded time-Varying Delay are derived.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this article, the authors present a secure state estimation algorithm that uses a satisfiability modulo theory approach to harness the complexity of the secure state estimator and provide guarantees on the soundness and completeness of the algorithm.
Abstract: Secure state estimation is the problem of estimating the state of a dynamical system from a set of noisy and adversarially corrupted measurements. Intrinsically a combinatorial problem, secure state estimation has been traditionally addressed either by brute force search, suffering from scalability issues, or via convex relaxations, using algorithms that can terminate in polynomial time but are not necessarily sound. In this paper, we present a novel algorithm that uses a satisfiability modulo theory approach to harness the complexity of secure state estimation. We leverage results from formal methods over real numbers to provide guarantees on the soundness and completeness of our algorithm. Moreover, we discuss its scalability properties, by providing upper bounds on the runtime performance. Numerical simulations support our arguments by showing an order of magnitude decrease in execution time with respect to alternative techniques. Finally, the effectiveness of the proposed algorithm is demonstrated by applying it to the problem of controlling an unmanned ground vehicle.

Journal ArticleDOI
TL;DR: It is proved that, when a simple LKF is applied, the stability criteria obtained by the Wirtinger-based inequality and the Jensen inequality are equivalent, which means that the tighter inequality does not always lead to a less conservative criterion.
Abstract: The bounding inequalities and the Lyapunov-Krasovskii functionals (LKFs) are important for the stability analysis of time-delay systems. Much attention has been paid to develop tighter inequalities for improving stability criteria, while the contribution of the LKFs has not been considered when discussing the relationship between the tightness of inequalities and the conservatism of criteria. This note is concerned with this issue. Firstly, it is proved that, when a simple LKF is applied, the stability criteria obtained by the Wirtinger-based inequality and the Jensen inequality are equivalent although the Wirtinger-based inequality is tighter. It means that the tighter inequality does not always lead to a less conservative criterion. Secondly, it is found that a suitable augmented LKF with necessary integral vectors in its derivative is required to achieve the advantage of the Wirtinger-based inequality. Based on this observation, two delay-product-type terms are introduced into the LKF to establish new stability criteria. Finally, a numerical example is given to verify the equivalence statements and to show the benefit of the proposed criteria.

Journal ArticleDOI
TL;DR: It is proved that all agents with any initial state can reach output consensus at an optimal solution to the given constrained optimization problem, provided that the graph describing the communication links among agents is undirected and connected.
Abstract: This technical note presents a continuous-time multi-agent system for distributed optimization with an additive objective function composed of individual objective functions subject to bound, equality, and inequality constraints. Each individual objective function is assumed to be convex in the region defined by its local bound constraints only without the need to be globally convex. All agents in the system communicate using a proportional-integral protocol with their output information instead of state information to reduce communication bandwidth. It is proved that all agents with any initial state can reach output consensus at an optimal solution to the given constrained optimization problem, provided that the graph describing the communication links among agents is undirected and connected. It is further proved that the system with only integral protocol is also convergent to the unique optimal solution if each individual objective function is strictly convex. Simulation results are presented to substantiate the theoretical results.

Journal ArticleDOI
TL;DR: A control design approach in the spatial domain is presented that achieves tracking of the desired spacing policy and guarantees disturbance string stability with respect to a spatially varying reference velocity.
Abstract: A novel delay-based spacing policy for the control of vehicle platoons is introduced together with a notion of disturbance string stability. The delay-based spacing policy specifies the desired intervehicular distance between vehicles and guarantees that all vehicles track the same spatially varying reference velocity profile, as is for example required for heavy-duty vehicles driving over hilly terrain. Disturbance string stability is a notion of string stability of vehicle platoons subject to external disturbances on all vehicles that guarantees that perturbations do not grow unbounded as they propagate through the platoon. Specifically, a control design approach in the spatial domain is presented that achieves tracking of the desired spacing policy and guarantees disturbance string stability with respect to a spatially varying reference velocity. The results are illustrated by means of simulations.

Journal ArticleDOI
TL;DR: This paper considers a linear network-reduced power system model along with an $\mathscr {H}_2$ performance metric accounting for the network coherency and provides a set of closed-form global optimality results for particular problem instances as a computational approach resulting in locally optimal solutions.
Abstract: A major transition in the operation of electric power grids is the replacement of synchronous machines by distributed generation connected via power electronic converters. The accompanying “loss of rotational inertia” and the fluctuations by renewable sources jeopardize the system stability, as testified by the ever-growing number of frequency incidents. As a remedy, numerous studies demonstrate how virtual inertia can be emulated through various devices, but few of them address the question of “where” to place this inertia. It is, however, strongly believed that the placement of virtual inertia hugely impacts system efficiency, as demonstrated by recent case studies. In this paper, we carry out a comprehensive analysis in an attempt to address the optimal inertia placement problem. We consider a linear network-reduced power system model along with an $\mathscr {H}_2$ performance metric accounting for the network coherency. The optimal inertia placement problem turns out to be non-convex, yet we provide a set of closed-form global optimality results for particular problem instances as well as a computational approach resulting in locally optimal solutions. Further, we also consider the robust inertia allocation problem, wherein the optimization is carried out accounting for the worst-case disturbance location. We illustrate our results with a three-region power grid case study and compare our locally optimal solution with different placement heuristics in terms of different performance metrics.

Journal ArticleDOI
TL;DR: In this paper, a distributed Nash equilibrium seeking strategy is proposed for non-cooperative games with non-quadratic payoffs, where multiple isolated Nash equilibria may coexist in the game.
Abstract: In this paper, Nash equilibrium seeking among a network of players is considered. Different from many existing works on Nash equilibrium seeking in noncooperative games, the players considered in this paper cannot directly observe the actions of the players who are not their neighbors. Instead, the players are supposed to be capable of communicating with each other via an undirected and connected communication graph. By a synthesis of a leader-following consensus protocol and the gradient play, a distributed Nash equilibrium seeking strategy is proposed for the noncooperative games. Analytical analysis on the convergence of the players’ actions to the Nash equilibrium is conducted via Lyapunov stability analysis. For games with nonquadratic payoffs, where multiple isolated Nash equilibria may coexist in the game, a local convergence result is derived under certain conditions. Then, a stronger condition is provided to derive a nonlocal convergence result for the nonquadratic games. For quadratic games, it is shown that the proposed seeking strategy enables the players’ actions to converge to the Nash equilibrium globally under the given conditions. Numerical examples are provided to verify the effectiveness of the proposed seeking strategy.

Journal ArticleDOI
TL;DR: This 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.
Abstract: 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.

Journal ArticleDOI
TL;DR: It is shown that both current-state and initial-state opacity problems in bounded Petri nets can be efficiently solved by using a compact representation of the reachability graph, called basis reachabilitygraph (BRG), which is practically efficient since the exhaustive enumeration of the Reachability space can be avoided.
Abstract: A system is said to be opaque if a given secret behavior remains opaque (uncertain) to an intruder who can partially observe system activities. This work addresses the verification of state-based opacity in systems modeled with Petri nets. The secret behavior of a system is defined as a set of states. More precisely, two state-based opacity properties are considered: current-state opacity and initial-state opacity . We show that both current-state and initial-state opacity problems in bounded Petri nets can be efficiently solved by using a compact representation of the reachability graph, called basis reachability graph (BRG). This approach is practically efficient since the exhaustive enumeration of the reachability space can be avoided.

Journal ArticleDOI
TL;DR: In this article, the convergence rate bound for Douglas-Rachford splitting and ADMM under strong convexity and smoothness assumptions is shown. And the convergence bound is tight for the class of problems under consideration for all feasible algorithm parameters.
Abstract: Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show global linear convergence rate bounds for Douglas-Rachford splitting and ADMM under strong convexity and smoothness assumptions. We further show that the rate bounds are tight for the class of problems under consideration for all feasible algorithm parameters. For problems that satisfy the assumptions, we show how to select step-size and metric for the algorithm that optimize the derived convergence rate bounds. For problems with a similar structure that do not satisfy the assumptions, we present heuristic step-size and metric selection methods.

Journal ArticleDOI
TL;DR: This technical note investigates the sliding mode control (SMC) design based on finite-time boundedness (FTB) for a class of nonlinear systems and develops a suitable SMC law to drive the state trajectories onto the specified sliding surface during a specified finite time interval.
Abstract: This technical note investigates the sliding mode control (SMC) design based on finite-time boundedness (FTB) for a class of nonlinear systems. A suitable SMC law is constructed to drive the state trajectories onto the specified sliding surface during a specified finite (possibly short ) time interval. Besides, by introducing a partitioning strategy , the corresponding FTB over reaching phase and sliding motion phase are guaranteed, respectively. And then, the sufficient conditions are derived to ensure the FTB of the closed-loop systems over the whole finite-time interval. Finally, a simulation example is given to show the effectiveness of the proposed design method.

Journal ArticleDOI
TL;DR: This paper studies the distributed optimization problem for continuous-time multiagent systems with general linear dynamics to cooperatively optimize a team performance function formed by a sum of convex local objective functions.
Abstract: This paper studies the distributed optimization problem for continuous-time multiagent systems with general linear dynamics. The objective is to cooperatively optimize a team performance function formed by a sum of convex local objective functions. Each agent utilizes only local interaction and the gradient of its own local objective function. To achieve the cooperative goal, a couple of fully distributed optimal algorithms are designed. First, an edge-based adaptive algorithm is developed for linear multiagent systems with a class of convex local objective functions. Then, a node-based adaptive algorithm is constructed to solve the distributed optimization problem for a class of agents satisfying the bounded-input bounded-state stable property. Sufficient conditions are given to ensure that all agents reach a consensus while minimizing the team performance function. Finally, numerical examples are provided to illustrate the theoretical results.

Journal ArticleDOI
TL;DR: A new time-dependent discontinuous Lyapunov functional, namely, free-matrix-based time- dependent discontinuous (FMBTDD) Lyapinov functional is introduced for stability analysis of sampled-data systems.
Abstract: In this paper, a new time-dependent discontinuous Lyapunov functional, namely, free-matrix-based time-dependent discontinuous (FMBTDD) Lyapunov functional is introduced for stability analysis of sampled-data systems. First, a modified free-matrix-based integral inequality (MFMBII) is derived based on the existing free-matrix-based integral inequality [1] and it is applied to develop a stability criterion for sampled-data systems. And then, inspired by MFMBII, FMBTDD term is established that leads to efficient stability conditions. Four numerical examples are given to demonstrate the effectiveness of the proposed methods.

Journal ArticleDOI
TL;DR: In this paper, a sliding mode observer design scheme is proposed for a new descriptor augmented plant and it is shown that the stabilization of the overall closed-loop plant can be guaranteed by the proposed fault tolerant control (FTC) scheme.
Abstract: This paper addresses the stabilization problem for nonlinear Markovian jump systems (MJS) with output disturbances, actuator and sensor faults simultaneously. This kind of plants are common in practical systems, such as mobile manipulators with switching joints. In this paper, a sliding mode observer design scheme is proposed for a new descriptor augmented plant. By employing the developed observer, the effects of actuator and sensor faults can be eliminated. It is shown that the stabilization of the overall closed-loop plant can be guaranteed by the proposed fault tolerant control (FTC) scheme. Finally, an example concerning mobile manipulators with Markovian switching joints is presented to show the effectiveness and applicability of the theoretical results.

Journal ArticleDOI
TL;DR: In this article, a distributed continuous-time projected algorithm for convex cost functions with local constraints is proposed, in which each agent knows its local cost function and local constraint set, and proves that all the agents of the algorithm can find the same optimal solution.
Abstract: This technical note studies the distributed optimization problem of a sum of nonsmooth convex cost functions with local constraints. At first, we propose a novel distributed continuous-time projected algorithm, in which each agent knows its local cost function and local constraint set, for the constrained optimization problem. Then we prove that all the agents of the algorithm can find the same optimal solution, and meanwhile, keep the states bounded while seeking the optimal solutions. We conduct a complete convergence analysis by employing nonsmooth Lyapunov functions for the stability analysis of differential inclusions. Finally, we provide a numerical example for illustration.