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 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.     

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.     

Hybrid consensus for multi-agent systems with time-driven jumps

In this paper, the behavior of scalar multi-agent systems over networks subject to time-driven jumps. Assuming that all agents communicate through distinct communication digraphs at jump and flow times, the asymptotic multi-consensus behavior of the hybrid network is explicitly characterized. The hybrid multi-consensus is shown to be associated with a suitable partition that is almost equitable for both the jump and flow communication digraphs. In doing so, no assumption on the underlying digraphs is introduced. Finally, the coupling rules making the multi-consensus subspace attractive are established. Several simulation examples illustrate the theoretical results.     

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.     

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.     

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.     

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.     

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.     

Randomly changing leader-following consensus control for Markovian switching multi-agent systems with interval time-varying delays

This paper considers the problem of leader-following consensus stability and also stabilization for multi-agent systems with interval time-varying delays. The randomly occurring interconnection information of the leader and the Markovian switching interconnection information of the agent are matters of concern in the systems. Through construction of a suitable Lyapunov–Krasovskii functional and utilization of the reciprocally convex approach, new delay-dependent consensus stability and stabilization conditions for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by using various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Finite-time consensus for switching network topologies with disturbances

In this paper we investigate the properties of a decentralized consensus algorithm for a network of continuous-time integrators subject to unknown-but-bounded time-varying disturbances. The proposed consensus algorithm is based on a discontinuous local interaction rule. Under certain restrictions on the switching topology, it is proven that after a finite transient time the agents achieve an approximated consensus condition by attenuating the destabilizing effect of the disturbances. This main result is complemented by an additional result establishing the achievement of consensus under different requirements on the switching communication topology. In particular, we provide a convergence result that encompasses situations in which the time varying graph is always disconnected. Lyapunov analyses are carried out to support the suggested algorithms and results. Simulative tests considering, as case study, the synchronization problem for a network of clocks are illustrated and commented on to validate the developed analysis.     

Sampled-data-based consensus of multi-agent systems under asynchronous denial-of-service attacks

This paper investigates the sampled-data-based consensus problem of multi-agent systems (MASs) under asynchronous denial-of-service (DoS) attacks. In order to describe asynchronous DoS attacks, a new definition of complete DoS attack and novel double-layer switched systems are proposed. A complete DoS attack refers to a DoS attack that consists of several consecutive successful DoS attacks. While a successful DoS attack denotes an attack that can break the connected communication topology into several isolated subgraphs. Based on this, the original system is transformed into a double-layer switched systems with a stable mode and several unstable modes. It should be pointed out that each unstable subsystem is also composed of finite second-level unstable subsystems that represent consecutive successful DoS attacks. Moreover, a new double-mode-dependent Lyapunov function (DMDLF) method is employed to obtain the lower and upper bounds of the corresponding average dwell time (ADT) of subsystems. It is proved that the consensus of MASs under asynchronous DoS attacks can be achieved by using the feedback consensus controllers which can be designed simultaneously. Finally, an illustrative example is provided to illustrate the effectiveness of the results proposed in this paper.     

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.     

Leader-following exponential consensus of general linear multi-agent systems via event-triggered control with combinational measurements

In this paper, the leader-following exponential consensus problem of general linear multi-agent systems via event-triggered control is considered. By using the combinational measurements, two classes of event triggers are designed, one depends on continuous communications between the agents, the other avoids continuous communications. For such two classes of event triggers, the exponential consensus as well as the convergence rates of the controlled multi-agent systems are studied, respectively, by employing the M-matrix theory, algebraic graph theory and the Lyapunov method.     

A note on the consensus finding problem in communication networks with switching topologies

In this note, we discuss the problem of consensus finding in communication networks of agents with dynamically switching topologies. In particular, we consider the case of directed networks with unbalanced matrices of communication rates. We formulate sufficient conditions for consensus finding in terms of strong connectivity of the underlying directed graphs and prove that, given these conditions, consensus is found asymptotically. Moreover, we show that this consensus is an emergent property of the system, being encoded in its dynamics and not just an invariant of its initial configuration.     

Formation control for second-order multi-agent systems with time-varying delays under directed topology

In this paper, we investigate a formation control problem for second-order multi-agent systems with directed graph interconnection topologies that contain time-varying coupling delays. By using a special multiple leaders’ framework, sufficient conditions are obtained for both time-invariant and time-varying formations as well as for time-varying formations for trajectory tracking, which guarantees the attainment of the formations is at exponentially converging speeds. Some numerical simulations are also conducted to validate the theoretical results.     

Analysis and stability of consensus in networked control systems

In this paper, the consensus problem in networks of integrators is investigated. After recalling the classical diffusive protocol, we present in a unified framework some results on the rate of convergence previously presented in the literature. Then, we introduce two switching communication protocols, one based on a switching coupling law between neighboring nodes, the other on the conditional activation of links in the network. We show that the former protocol induces the monotonicity of each system in the network, enhancing the speed of convergence to consensus. Moreover, adopting this novel protocol, we are able to control the network, steering the nodes’ dynamics to a desired consensus value. The aim of the latter protocol is instead to select adaptively the activation of the edges of the network, in accordance with the dynamics of the network. After showing the effectiveness of both approaches through numerical simulations, the stability properties of these protocols are discussed.     

Distributed consensus in noncooperative inventory games

This paper deals with repeated nonsymmetric congestion games in which the players cannot observe their payoffs at each stage. Examples of applications come from sharing facilities by multiple users. We show that these games present a unique Pareto optimal Nash equilibrium that dominates all other Nash equilibria and consequently it is also the social optimum among all equilibria, as it minimizes the sum of all the players’ costs. We assume that the players adopt a best response strategy. At each stage, they construct their belief concerning others probable behavior, and then, simultaneously make a decision by optimizing their payoff based on their beliefs. Within this context, we provide a consensus protocol that allows the convergence of the players’ strategies to the Pareto optimal Nash equilibrium. The protocol allows each player to construct its belief by exchanging only some aggregate but sufficient information with a restricted number of neighbor players. Such a networked information structure has the advantages of being scalable to systems with a large number of players and of reducing each player’s data exposure to the competitors.