Impulsive consensus of one-sided Lipschitz nonlinear multi-agent systems with Semi-Markov switching topologies

Many real systems involve not only parameter changes but also sudden variations in environmental conditions, which often causes unpredictable topologies switching. This paper investigates the impulsive consensus problem of the one-sided Lipschitz nonlinear multi-agent systems (MASs) with Semi-Markov switching topologies. Different from the existing modeling methods of the Markov chain, the Semi-Markov chain is adopted to describe this kind of randomly occurring changes reasonably. To cope with the communication and control cost constraints in the multi-agent systems, the distributed impulsive control method is applied to address the leader–follower consensus problem. Beyond that, to obtain a wider nonlinear application range, the one-sided condition is delicately developed to the controller design, and the results are different from the ones obtained in the traditional method with the Lipschitz condition (note that the existing results are usually only applicable to the case with small Lipschitz constant). Based on the characteristics of cumulative distribution functions, the theory of Lyapunov-like function and impulsive differential equation, the asymptotically mean square consensus of multi-agent systems is maintained with the proposed impulsive control protocol. Finally, an explanatory simulation is presented to validate the correctness of the proposed approach conclusively.     

Impulsive consensus problem of second-order multi-agent systems with switching topologies

The paper proposes an impulsive consensus protocol to solve the consensus problem of the second-order multi-agent systems with fixed and switching topologies. Some sufficient conditions are obtained for the states of follower agents converging to the state of leader asymptotically. Two numerical simulations are also given to verify the effectiveness of the theoretical analysis.     

Impulsive control for one-side Lipschitz nonlinear MASs under semi-Markovian switching topologies with partially unknown transition probabilities

This article addresses the consensus problem of impulsive control for the multi-agent systems under uncertain semi-Markovian switching topologies. Considering the control and information exchanging cost in the implementation of multi-agent systems, an impulsive control protocol is developed not only to relieve the network burden but address the consensus problem. In addition, globally Lipschitz condition, as required in many existing literatures, is not needed in this article, so we introduce one-side Lipschitz condition to loosen the constraint of Lipschitz constant and widen the range of nonlinear application. According to cumulative distribution functions and Lyapunov functional, sufficient criteria are derived for the mean square consensus of multi-agent systems. It is shown that the impulsive sequence is not only inconsistent with switching sequence but also mode-dependent. Finally, simulation results are given to validate the superiority of the theoretical results.     

Tracking consensus of nonlinear MASs with asymmetric communication delays in noisy environments

This paper investigates the tracking consensus problem of nonlinear multi-agent systems (MASs) with asymmetric time-varying communication delays in noisy environments under the conditions of fixed and switching directed topologies. A novel stochastic analysis approach is proposed, which guarantees that the designed two distributed tracking protocols can guide the controlled systems to achieve tracking consensus in the sense of mean square. In order to further reveal the influence of asymmetric communication delays on the tracking consensus ability for MASs, some new delay-dependent sufficient conditions for mean-square consensus are also developed. A simple example is finally given to illustrate the effectiveness of the proposed theoretical results.     

Variable impulsive consensus of nonlinear multi-agent systems

In this paper, the consensus problem for nonlinear multi-agent systems with variable impulsive control method is studied. In order to decrease the communication wastage, a novel distributed impulsive protocol is designed to achieve consensus. Compared with the common impulsive consensus method with fixed impulsive instants, the variable impulsive consensus method proposed in this paper is more flexible and reliable in practical application. Based on Lyapunov stability theory and some inequality techniques, several novel impulsive consensus conditions are obtained to realize the consensus of multi-agent systems. Finally, some necessary simulations are performed to validate the effectiveness of theoretical results.     

Impulsive consensus in directed networks of identical nonlinear oscillators with switching topologies

In this paper, we investigate the problem of impulsive consensus of multi-agent systems, where each agent can be modeled as an identical nonlinear oscillator. Firstly, an impulsive control protocol is designed for directed networks with switching topologies based on the local information of agents. Then sufficient conditions are given to guarantee the consensus of the networked nonlinear oscillators. How to select the discrete instants and impulsive constants is also discussed. Numerical simulations show the effectiveness of our theoretical results.     

Impulsive consensus of multi-agent systems with stochastically switching topologies

In this paper, the impulsive consensus problem for multi-agent systems is investigated. The purpose of this paper is to provide a valid consensus protocol that overcomes the difficulty caused by stochastically switching structures via impulsive control. Some sufficient conditions of almost sure consensus are proposed when the switching structures are the independent process or the Markov process. It is shown that the sum-zero rows of matrix play a key role in achieving group consensus. Furthermore, simulation examples are provided to illustrate and visualize the effectiveness of these results.     

Further improvement of finite-time consensus protocols for detail-balanced networks

This paper presents a new class of protocols to solve finite-time consensus for multi-agent systems. The protocols are induced from the classical finite-time consensus algorithm by using the so-called protocol function. Sufficient conditions are established for networked agents to experience finite-time consensus under time-varying undirected and fixed directed topologies. Numerical simulations show that the proposed protocols can provide more flexibility to improve convergence rate.     

Leaderless and leader-following consensus of multi-agent chaotic systems with unknown time delays and switching topologies

In this paper the distributed consensus problem for a class of multi-agent chaotic systems with unknown time delays under switching topologies and directed intermittent communications is investigated. Each agent is modeled as a general nonlinear system including many chaotic systems with or without time delays. Based on the Lyapunov stability theory and graph theory, some sufficient conditions guarantee the exponential convergence. A graph-dependent Lyapunov proof provides the definite relationship among the bound of unknown time delays, the admissible communication rate and each possible topology duration. Moreover, the relationship reveals that these parameters have impacts on both the convergence speed and control cost. The case with leader-following communication graph is also addressed. Finally, simulation results verify the effectiveness of the proposed method.     

Leader-following finite-time consensus for multi-agent systems with jointly-reachable leader

Finite-time consensus problems of the leader-following multi-agent systems with jointly-reachable leader and switching jointly-reachable leader are studied in this paper. Based on the graph theory, LaSalle’s invariance principle and Lyapunov stability theory, the finite-time consensus protocols are presented for the first-order and second-order leader-following systems. Some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.     

Second-order cluster consensus of multi-agent dynamical systems with impulsive effects

This paper discuss the cluster consensus of multi-agent dynamical systems (MADSs) with impulsive effects and coupling delays. Some sufficient conditions that guarantee cluster consensus in MADS are derived. In each cluster, agents update their position and velocity states according to a leader’s instantaneous information, and interactions among agents are uncertain. Furthermore, switching topology problem in MADS is considered by impulsive stability and adaptive strategy. Finally, numerical simulations are given to verify our theoretical analysis.     

Dynamic output feedback consensus of continuous‐time networked multiagent systems

This article addresses the dynamic output feedback consensus problem of continuous‐time networked multiagent systems. Both a fixed topology and Markovian switching topologies are considered. The consensus algorithms are on the base of the output information of each agent's itself and its neighbors. Some sufficient conditions for consensus of multiagent systems are obtained in forms of bilinear matrix inequalities. The algorithm based on the homotopy continuation method is given to compute the feasible controller gains. Numerical simulations are given to show the effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 20: 35–42, 2015     

基于马尔科夫拓扑切换和随机通信干扰的连续时间多自主体系统的趋同控制

研究了基于不可靠通信网络的连续时间多自主体系统的趋同控制.自主体间的通信信道受高斯噪声干扰;不可靠通信因素导致的网络拓扑随机切换由马氏链刻画.为克服随机噪声和马尔科夫拓扑切换的影响,设计了随机逼近型趋同协议;基于马氏跳参数随机微分方程稳定性理论、代数图理论、连续鞅和马氏链理论,证明了多自主体系统实现渐近无偏均方平均趋同...     

On optimal control problems of a class of impulsive switching systems with terminal states constraints

The global optimal control problem is proposed for a special class of hybrid dynamical systems, i.e. impulsive switching systems. Then the necessary condition of the above problem, the minimum principle, is given. Ekeland’s variational principle and the matrix cost functional structure expression are utilized in the process of the proof. Based on the main result, a special linear hybrid impulsive and switching system (HISS) is illustrated and the optimal control algorithm is presented. Moreover, the cases of pure impulsive systems and pure switched systems are included in this paper.     

Exponential stability and applications of switched positive linear impulsive systems with time-varying delays and all unstable subsystems

The global uniform exponential stability of switched positive linear impulsive systems with time-varying delays and all unstable subsystems is studied in this paper, which includes two types of distributed time-varying delays and discrete time-varying delays. Switching behaviors dominating the switched systems can be either stabilizing and destabilizing in the new designed switching sequence. We design new linear programming algorithm process to find the feasible ratio of stabilizing switching behaviors, which can be compensated by unstable subsystems, destabilizing switching behaviors, and impulses. Specically, we add a kind of nonnegative impulses which is consistent with the switching behaviors for the systems. Employing a multiple co-positive Lyapunov-Krasovskii functional, we present several new sufficient stability criteria and design new switching sequence. Then, we apply the obtained stability criteria to the exponential consensus of linear delayed multi-agent systems, and obtain the new exponential consensus criteria. Three simulations are provided to demonstrate the proposed stability criteria.     

Distributed impulsive control consensus for a class of unknown nonlinear multi-agent systems based on event-triggered scheme

In this study, we are concerned with the impulsive consensus control problem for a class of nonlinear multi-agent systems (MASs) which have unknown dynamics and directed communication topology. The neural networks (NNs) method is the first utilized to construct distributed event-triggered impulsive consensus protocol. In contrast to the existing impulsive consensus protocol, the consensus protocol proposed in this paper does not need the dynamics of agents, which enhances the system robustness, and realizes distributed event-triggered communication between agents, which can reduce unnecessary consumption of communication resources. Sufficient conditions are derived to ensure the consensus of the controlled MASs and the exclusion of Zeno-behavior. Finally, simulation examples are presented to illustrate the effectiveness of the proposed control protocol.     

On consensus speed of multi-agent systems with double-integrator dynamics

The performance of multi-agent systems is an important issue. In this paper, it is focused on consensus speed for multi-agent systems with double-integrator dynamics and fixed undirected graphes under a kind of consensus protocols. It is revealed that, under some conditions, the maximum consensus speed is determined by the largest and the smallest nonzero eigenvalues of the Laplacian matrix of the undirected connected graph. Based on the mentioned results, arbitrary desired consensus speed can be achieved by choosing suitable feedback gains. Numerical simulations are given to illustrate the main results.     

Control vector Lyapunov functions for large-scale impulsive dynamical systems

Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we provide generalizations to the recent extensions of vector Lyapunov theory for continuous-time systems to address stability and control design of impulsive dynamical systems via vector Lyapunov functions. Specifically, we provide a generalized comparison principle involving hybrid comparison dynamics that are dependent on the comparison system states as well as the nonlinear impulsive dynamical system states. Furthermore, we develop stability results for impulsive dynamical systems that involve vector Lyapunov functions and hybrid comparison inequalities. Based on these results, we show that partial stability for state-dependent impulsive dynamical systems can be addressed via vector Lyapunov functions. Furthermore, we extend the recently developed notion of control vector Lyapunov functions to impulsive dynamical systems. Using control vector Lyapunov functions, we construct a universal hybrid decentralized feedback stabilizer for a decentralized affine in the control nonlinear impulsive dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel. These results are then used to develop hybrid decentralized controllers for large-scale impulsive dynamical systems with robustness guarantees against full modeling and input uncertainty.     

Finite-time semistability,Filippov systems,and consensus protocols for nonlinear dynamical networks with switching topologies

This paper focuses on semistability and finite-time semistability for discontinuous dynamical systems. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. In this paper, we extend the theory of semistability to discontinuous autonomous dynamical systems. In particular, Lyapunov-based tests for strong and weak semistability as well as finite-time semistability for autonomous differential inclusions are established. Using these results we then develop a framework for designing semistable and finite-time semistable protocols for dynamical networks with switching topologies. Specifically, we present distributed nonlinear static and dynamic output feedback controller architectures for multiagent network consensus and rendezvous with dynamically changing communication topologies.     

Second-order consensus for heterogeneous multi-agent systems in the cooperation–competition network: A hybrid adaptive and pinning control approach

In this paper, a second-order consensus problem is investigated for the heterogeneous agents in the cooperation–competition network, with the parameters of the agents’ dynamics being uncertain. By introducing an exosystem, a hybrid adaptive and pinning control strategy is firstly proposed to ensure that all the agents follow a desired trajectory which is a function of the exosystem state. Several effective sufficient conditions are obtained by applying algebraic graph theory and the Barbalat lemma. Besides, the switching topologies between the competition agents are also considered. With the help of the Barbalat-like lemma, it is found that second-order consensus problem of the heterogeneous agents can be solved even when the competition sub-network is dynamic. Finally, simulation results are presented to validate the effectiveness of the theoretical analysis.