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.     

Consensus seeking in multi-agent systems via hybrid protocols with impulse delays

This paper studies the consensus problem of multi-agent systems with both fixed and switching topologies. A hybrid consensus protocol is proposed to take into consideration of continuous-time communications among agents and delayed instant information exchanges on a sequence of discrete times. Based on the proposed algorithms, the multi-agent systems with the hybrid consensus protocols are described in the form of impulsive systems or impulsive switching systems. By employing results from matrix theory and algebraic graph theory, some sufficient conditions for the consensus of multi-agent systems with fixed and switching topologies are established, respectively. Our results show that, for small impulse delays, the hybrid consensus protocols can solve the consensus problem if the union of continuous-time and impulsive-time interaction digraphs contains a spanning tree frequently enough. Simulations are provided to demonstrate the effectiveness of the proposed consensus protocols.     

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.     

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.     

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 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.     

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.     

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.     

不确定二阶多智能体系统的鲁棒最优一致

针对不确定二阶多智能体系统,研究了其鲁棒最优一致性问题.首先,基于每个智能体所获得的邻居信息,设计了一个使多智能体系统达到一致的控制协议.其次,研究了多智能体系统的最优一致性问题,给出了系统在满足一定性能指标下达到一致的条件.再次,基于该条件,利用Schur补引理和线性矩阵不等式技术,给出了不确定系统达到鲁棒最优一致的条件.最后,通过仿真验证了所得结果的可行性.     

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.     

Adaptive‐impulsive function projective synchronization for a class of time‐delay chaotic systems

This article investigates the function projective synchronization (FPS) for a class of time‐delay chaotic system via nonlinear adaptive‐impulsive control. To achieve the FPS, suitable nonlinear continuous and impulsive controllers are designed based on adaptive control theory and impulsive control theory. Using the generalized Babarlat's lemma, a general condition is given to ensure the FPS. Here, the time‐delay chaotic system is assumed to satisfy the Lipschitz condition while the Lipschitz constants are estimated by augmented adaptation equations. Numerical simulation results are also presented to verify the effectiveness of the proposed synchronization scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 333–341, 2015     

Distributed adaptive switching consensus control of heterogeneous multi-agent systems with switched leader dynamics

In this paper, the leader-following distributed consensus control problem is addressed for general linear multi-agent systems with heterogeneous uncertain agent dynamics and switched leader dynamics. Different from most existing results with a single linear time-invariant (LTI) leader dynamics, the leader dynamics under consideration is composed by a family of LTI models and a switching logic governing the switches among them, which is capable of generating more diverse and sophisticated reference signals to accommodate more complicated consensus control design tasks. A novel distributed adaptive switching consensus protocol is developed by incorporating the model reference adaptive control mechanism and arbitrary switching control technique, which can be synthesized by following a two-layer hierarchical design scheme. A numerical example has been used to demonstrate the effectiveness of the proposed approach.     

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.     

CONSENSUS OF THE SECOND-ORDER MULTI-AGENT SYSTEMS WITH AN ACTIVE LEADER AND COUPLING TIME DELAY

This article investigates the consensus problem of the second-order multi-agent systems with an active leader and coupling time delay in direct graph. One decentralized state control rule is constructed for each agent to track the active leader and it is proved that the proposed control scheme enables the consensus to be obtained when the adjacency topology is fixed/switched. Simulation results show effectiveness of the proposed theoretical analysis.     

Consensus of the second-order multi-agent systems with an active leader and coupling time delay

This article investigates the consensus problem of the second-order multi-agent systems with an active leader and coupling time delay in direct graph. One decentralized state control rule is constructed for each agent to track the active leader and it is proved that the proposed control scheme enables the consensus to be obtained when the adjacency topology is fixed/switched. Simulation results show effectiveness of the proposed theoretical analysis.     

一阶多智能体系统的一致性分析

研究一阶连续多智能体系统的一致性问题,其中每个智能体只能在一系列离散时刻上获得其相对邻居的状态信息,并且每个智能体的保持器的周期和采样器的周期是不同的.通过分析多智能体系统的稳定性,获得了一致性成立的充要条件,该条件揭示了交流拓扑、控制器增益、采样器的周期和保持器的周期的关系.最后,提供一个仿真例子以说明理论结果的有效性.     

Stability of complex-valued impulsive and switching system and application to the Lü system

In this paper, the stability of complex-valued impulsive and switching system is addressed. By using switched Lyapunov functions on a complex field, some new stability criteria of complex-valued impulsive and switching systems are established, which not only generalize some known results in the literature, but also greatly reduce the complexity of analysis and computation. As an application, a new hybrid impulsive and switching feedback controller for the complex-valued chaotic Lü system is designed.     

Iterative learning consensus control with initial state learning for fractional order distributed parameter models multi-agent systems

This paper considers the consensus control problem of multi-agent systems (MAS) with distributed parameter models. Based on the framework of network topologies, a second-order PI-type iterative learning control (ILC) protocol with initial state learning is proposed by using the nearest neighbor knowledge. A discrete system for proposed ILC is established, and the consensus control problem is then converted to a stability problem for such a discrete system. Furthermore, by using generalized Gronwall inequality, a sufficient condition for the convergence of the consensus errors between any two agents is obtained. Finally, the validity of the proposed method is verified by two numerical examples.     

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.