Robust and nonfragile consensus of positive multiagent systems via observer‐based output‐feedback protocols

This article investigates the consensus problem for positive multiagent systems via an observer‐based dynamic output‐feedback protocol. The dynamics of the agents are modeled by linear positive systems and the communication topology of the agents is expressed by an undirected connected graph. For the consensus problem, the nominal case is studied under the semidefinite programming framework while the robust and nonfragile cases are investigated under the linear programming framework. It is required that the distributed state‐feedback controller and observer gains should be structured to preserve the positivity of multiagent systems. Necessary and/or sufficient conditions for the analysis of consensus are obtained by using positive systems theory and graph theory. For the nominal case, necessary and sufficient conditions for the codesign of state‐feedback controller and observer of consensus are derived in terms of matrix inequalities. Sufficient conditions for the robust and nonfragile consensus designs are derived and the codesign of state‐feedback controller and observer can be obtained in terms of solving a set of linear programs. Numerical simulations are provided to show the effectiveness and applicability of the theoretical results and algorithms.     

Pseudo-Predictor Feedback Control for Multiagent Systems with Both State and Input Delays

This paper is concerned with the consensus problem for high-order continuous-time multiagent systems with both state and input delays. A novel approach referred to as pseudo-predictor feedback protocol is proposed. Unlike the predictor-based feedback protocol which utilizes the open-loop dynamics to predict the future states, the pseudo-predictor feedback protocol uses the closed-loop dynamics of the multiagent systems to predict the future agent states. Full-order/reduced-order observer-based pseudo-predictor feedback protocols are proposed, and it is shown that the consensus is achieved and the input delay is compensated by the proposed protocols. Necessary and sufficient conditions guaranteeing the stability of the integral delay systems are provided in terms of the stability of the series of retarded-type time-delay systems. Furthermore, compared with the existing predictor-based protocols, the proposed pseudo-predictor feedback protocol is independent of the input signals of the neighboring agents and is easier to implement. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approaches.      

Output feedback semiglobal practical consensus of linear systems with relative state‐dependent uncertainties

This paper proposes an output feedback consensus control law for linear multiagent systems with relative state‐dependent uncertainties. To achieve output feedback control and uncertainty attenuation, the theories of extended high‐gain observer and structural decomposition are employed. Under the proposed control scheme, semiglobal practical consensus is achieved in the sense that the synchronization errors are ultimately bounded. Besides, the synchronization errors can be kept arbitrarily small by a proper choice of tuning parameters. Finally, a simulation example is provided to verify the theoretical results.     

Event‐triggered global leader‐following consensus of a group of neutrally stable linear systems subject to input saturation

This paper studies the global leader‐following consensus problem for a multiagent system using event‐triggered linear feedback control laws. The leader agent is described by a neutrally stable linear system and the follower agents are also described by a neutrally stable linear system but with saturating input. Both the state‐feedback case and the output‐feedback case are considered. In each case, an event‐triggered control law is constructed for each follower agent and an event‐triggering strategy is designed for updating these control laws. These event‐triggered control laws are shown to achieve global leader‐following consensus when the communication topology among the follower agents is strongly connected and detailed balanced and the leader is a neighbor of at least one follower agent. The Zeno behavior is excluded. The theoretical results are illustrated by simulation.     

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

Adaptive Output‐Feedback Control of Nonlinear Systems with Multiple Uncertainties

This paper addresses the global stabilization via adaptive output‐feedback for a class of uncertain nonlinear systems. Remarkably, the systems under investigation are with multiple uncertainties: unknown control directions, unknown growth rates and unknown input bias, and can be used to describe more physical plants. Multiple uncertainties, which usually cannot be compensated by a sole compensation technique, may give rise to big technical difficulty for controller design. To overcome such difficulty and to achieve the global stabilization, a new adaptive output‐feedback scheme is proposed in this paper, by flexibly combining Nussbaum‐type function, tuning function technique and extended state observer. It is shown that, under the designed controller, the system states globally converge to zero. A simulation example on non‐zero set‐point regulation is given to demonstrate the effectiveness of the theoretical results.     

Adaptive neural control for multiagent systems with asymmetric time‐varying state constraints and input saturation

This article investigates the leader‐follower consensus problem of a class of non‐strict‐feedback nonlinear multiagent systems with asymmetric time‐varying state constraints (ATVSC) and input saturation, and an adaptive neural control scheme is developed. By introducing the distributed sliding‐mode estimator, each follower can obtain the estimation of leader's trajectory and track it directly. Then, with the help of time‐varying asymmetric barrier Lyapunov function and radial basis function neural networks, the controller is designed based on backstepping technique. Furthermore, the mean‐value theorem and Nussbaum function are utilized to address the problems of input saturation and unknown control direction. Moreover, the number of adaptive laws is equal to that of the followers, which reduces the computational complexity. It is proved that the leader‐follower consensus tracking control is achieved without violating the ATVSC, and all closed‐loop signals are semiglobally uniformly ultimately bounded. Finally, the simulation results are provided to verify the effectiveness of the control scheme.     

Robust semi‐global coordinated tracking of linear multi‐agent systems with input saturation

This paper investigates the problem of coordinated tracking of a linear multi‐agent system subject to actuator magnitude saturation and dead zone characteristic with input additive uncertainties and disturbances. Distributed consensus and swarm tracking protocols are developed from a low‐and‐high gain feedback approach. Under the assumption that each agent is asymptotically null controllable with bounded controls, it is shown that robust semi‐global consensus tracking and swarm tracking of the multi‐agent system can always be reached provided that the networks are connected. Numerical examples are provided to illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Fixed‐time output‐feedback consensus tracking control for second‐order multiagent systems

This paper is concerned with the problem of fixed‐time consensus tracking control for a class of second‐order multiagent systems under an undirected communication graph. A distributed output‐feedback fixed‐time consensus tracking control scheme is proposed to make the states of all individual agents simultaneously track a time‐varying reference state even when the reference state is available only to a subset of the group members and only output measurements are available for feedback. Homogeneous Lyapunov function and homogeneity property are employed to show that the control scheme can guarantee the consensus tracking errors converging the origin in finite time which is bounded by a fixed constant independent of initial conditions. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control law.     

Semi‐global bipartite output consensus of heterogeneous multi‐agent systems subject to input saturation by finite‐time observer

In this paper, the semi‐global bipartite output consensus problem of heterogeneous linear multi‐agent systems is studied. Compared with related works, both cooperative interactions and antagonistic interactions between agents are considered, and the input saturation on each follower is taken into account. First, two distributed finite‐time observers are designed to recover the leader's state. Particularly, the setting time can be independent of any initial states. Due to the antagonistic interactions, estimation values are the same as the leader's state in modulus but may not in sign. Then, the low‐gain feedback technique is used to develop the distributed control law for each follower. Moreover, we summarize a framework for solving the semi‐global bipartite output consensus problem of heterogeneous multi‐agent systems subject to input saturation. Finally, examples are given to illustrate the results.     

Active fault‐tolerant consensus control of Lipschitz nonlinear multiagent systems

This article investigates the active fault‐tolerant consensus problem for Lipschitz nonlinear multiagent systems under detailed balanced directed graph and actuator faults. First, a fault detection filter for each agent is designed, and all agents can be divided into two categories: healthy agents and possibly faulty agents. Second, fully distributed adaptive fault‐tolerant consensus protocols for healthy and possibly faulty agents are proposed to achieve state consensus. Third, based on the fault detection method and fault‐tolerant consensus protocols, active fault‐tolerant consensus algorithms are given. Simulation examples are presented to verify the effectiveness of the proposed active fault‐tolerant algorithms.     

Observer‐based adaptive control for nonlinear strict‐feedback stochastic systems with output constraints

In this paper, an adaptive output‐feedback control problem is investigated for nonlinear strict‐feedback stochastic systems with input saturation and output constraint. A barrier Lyapunov function is used to solve the problem of output constraint. Then, fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. To overcome the difficulties in designing the control signal in the saturation, we introduce an auxiliary signal in the n + 1th step in the deduction. By combining Nussbaum technique and the adaptive backstepping technique, an adaptive output‐feedback control method is developed. The proposed control method not only overcomes the problem of the compensation for the nonlinear term from the input saturation but also overcomes the problem of unavailable state measurements. It is proved that all the signals of the closed‐loop system are semiglobally uniformly ultimately bounded. Finally, the effectiveness of the proposed method is verified by the simulation results.     

Distributed finite‐time tracking of multiple Euler–Lagrange systems without velocity measurements

This paper investigates the distributed finite‐time tracking problem of networked agents with multiple Euler–Lagrange dynamics. To achieve finite‐time tracking, a distributed finite‐time protocol is first proposed on the basis of both relative position and relative velocity measurements. By using tools from homogeneous theory, it is theoretically shown that the proposed protocol can guarantee finite‐time tracking in the presence of control input constraints. On the basis of the state feedback analysis and with the aid of second‐order sliding‐mode observer approach, a new class of finite‐time tracking protocols based only on the relative position measurements is developed and employed. It is proved that the multiple agents equipped with the designed protocols can track the target location in finite time. Furthermore, a decentralized finite‐time protocol based on a distributed estimator is proposed to solve the finite‐time tracking problems with a dynamic leader. The effectiveness of the theoretical results is finally illustrated by numerical simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Semi‐global leader‐following consensus of discrete‐time linear multi‐agent systems subject to actuator position and rate saturation

This paper deals with the leader‐following consensus of discrete‐time multi‐agent systems subject to both position and rate saturation. Each agent is described by a discrete‐time general linear dynamic with actuator subject to position and rate saturation. A modified algebraic Riccati equation and low‐gain feedback design technique are used to construct both state feedback and output feedback control protocols. It is established that a semi‐global leader‐following consensus can be achieved when the system is asymptotically null controllable with bounded controls and a leader agent has a directed path to every follower agent. Finally, several simulations are carried out to illustrate the results. Copyright © 2016 John Wiley & Sons, Ltd.     

Internal model approach to cooperative robust output regulation for linear uncertain time‐delay multiagent systems

In this paper, we study the cooperative robust output regulation problem for linear uncertain multiagent systems with both communication delay and input delay by the distributed internal model approach. The problem includes the leader‐following consensus problem of linear multiagent systems with time delay as a special case. We first generalize the internal model design method to systems with both communication delay and input delay. Then, under a set of standard assumptions, we have obtained the solution to the problem via both the state feedback control law and the output feedback control law. In contrast to the existing results, our results apply to general linear uncertain multiagent systems, accommodate a large class of leader signals, and achieve asymptotic tracking and disturbance rejection at the same time.     

Observer‐based leaderless and leader‐following consensus for multiagent systems: A modified integral‐type event‐triggered design

This article aims to solve leaderless and leader‐following consensus problems for general linear systems by integral‐type event‐triggered control method. Different from the existing integral‐type event‐triggered controllers for multiagent systems (MASs), a modified distributed integral‐type event‐triggered scheme is designed via defining a measurement error without continuous communication. Then, distributed event‐triggered protocols are proposed for MASs to achieve the leaderless and leader‐following consensus. Moreover, for the case that all the agents' states are not available, distributed observers are given to estimate the full states. Meanwhile, leaderless and leader‐following consensus problems are investigated based on the observer‐based event‐triggered schemes. In addition, no agent will exhibit Zeno behavior. Finally, simulations are given to verify the effectiveness of our results.     

Robust consensus tracking of linear multiagent systems with input saturation and input‐additive uncertainties

The problem of robust global consensus tracking of linear multiagent systems with input saturation and input‐additive uncertainties is investigated in this paper. By using the parametric Lyapunov equation approach and an existing dynamic gain scheduling technique, a new distributed nonlinear‐gain scheduling consensus‐trackining algorithm is developed to solve this problem. Under the assumption that each agent is asymptotically null controllable with bounded control, it is shown that the robust global consensus tracking can be achieved under the undirected graph provided that its generated graph contains a directed spanning tree. Compared with the existing algebraic Riccati equation approach, which requires the online solution of a parameterized algebraic Riccati equation, all the parameters in the proposed nonlinear algorithm are offline determined a priori. Finally, numerical examples are provided to validate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Observer‐based consensus control of nonlinear multiagent systems under semi‐Markovian switching topologies and cyber attacks

This article investigates the leader‐following consensus of nonlinear multiagent systems under semi‐Markovian switching topologies and cyber attacks. Unlike the related works, the communication channels considered herein are subjected to successful but recoverable attacks, and when the channels work well, the network topology is time‐varying and described by a semi‐Markovian switching topology. Due to the effect of attacks, the communication network is intermittently paralyzed. For the cases that the transition rates of semi‐Markovian switching topologies are completely known and partially unknown, observer‐based control protocols and sufficient conditions are proposed, respectively, to ensure the consensus of the systems in the mean square sense. Finally, simulation examples are given to illustrate the validity of the theoretical results.     

Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

In this paper, a two‐stage control procedure is proposed for stabilization of a class of strict‐feedback systems with unknown constant time delays and nonlinear uncertainties in the input. A nominal controller is first designed to compensate input time delays without considering input nonlinear uncertainties. Extended from backstepping algorithm, input delay compensation is realized by means of predicted states that are computed through integration of cascaded system dynamics, making the nominal closed‐loop system asymptotically stable. Based on the nominal controller presented for the input delay system, a multi‐timescale system is subsequently developed to estimate the unknown input nonlinearity and make the estimate approach the nominal control input as fast as possible. It is proved that the proposed control scheme can make states of the strict‐feedback systems converge to zero and all the signals of the closed‐loop systems are guaranteed to be bounded in the presence of input time delays and nonlinear uncertainties. Simulation verification is carried out to illuminate the effectiveness of the proposed control approach.     

Distributed event‐triggered fixed‐time consensus for leader‐follower multiagent systems with nonlinear dynamics and uncertain disturbances

This paper focuses on the distributed event‐triggered fixed‐time consensus control problem of leader‐follower multiagent systems with nonlinear dynamics and uncertain disturbances. Two distributed fixed‐time consensus protocols are proposed based on distributed event‐triggered strategies, which can substantially reduce energy consumption and the frequency of the controller updates. It is proved that under the proposed distributed event‐triggered consensus tracking control strategies, the Zeno behavior is avoided. Compared with the finite‐time consensus tracking, the fixed‐time consensus tracking can be achieved within a settling time regardless of the initial conditions. Finally, 2 examples are performed to validate the effectiveness of the distributed event‐triggered fixed‐time consensus tracking controllers.