Markovian Switching Topologies Research Articles

Dynamic event‐triggered leader‐following consensus of nonlinear multi‐agent systems with measurement noises

AbstractThis paper investigates a leader‐following consensus problem for nonlinear multi‐agent systems (MASs) with measurement noises under fixed and Markovian switching topologies, respectively. Noises are considered when each agent measures the states of its neighbours, where intensities of noises are vector functions of relative states. To alleviate the utilization of communication and computation resources, a dynamic event‐triggered consensus protocol is designed, where the coupling strength is restricted in a given interval. By using the stochastic stability theorem, it is shown that leader‐following consensus is achieved under fixed topology, where an estimation of the convergence rate is given. Moreover, the problem is studied under switching topologies subjecting to the Markovian process, which is applicable to practical situations with a time‐varying communication environment. Finally, simulation examples are given to show the correctness of the proposed results.

Event-triggered group consensus for one-sided Lipschitz multi-agent systems with input saturation

This paper investigates event-triggered group consensus problem for multi-agent systems with input saturation under fixed topology and Markovian switching topologies respectively. The agent dynamics is described by one-sided Lipschitz nonlinear function, which covers a broad family of nonlinear systems and includes the well-known Lipschitz system as a special case. A novel distributed dynamic event-triggered communication scheme is proposed based on the local stochastic sampling information among the agents, which includes some existing schemes as special cases. A new stochastic sampled-data dependent error system is obtained by model transformation, based on the discontinuous Lyapunov stability theory, some local group consensus criteria in mean square can be derived for fixed topology and Markovian switching topologies, respectively. Moreover, an optimization algorithm is introduced to estimate the region of initial conditions. Finally, two specific numerical examples are employed to illustrate the effectiveness of the theoretical results.

Finite-time average consensus of directed second-order multi-agent systems with Markovian switching topology and impulsive disturbance

Finite-time average consensus of directed second-order multi-agent systems with Markovian switching topology and impulsive disturbance

Fault-Tolerant Formation Control for Multiple Stochastic AUV System under Markovian Switching Topologies

Formation control, which is a core problem in multi-autonomous underwater vehicle (AUV) systems, plays an important role in realizing safe and accurate cooperation of multi-AUV systems. This paper provides a study on fault-tolerant formation control for multiple stochastic AUV systems under Markovian switching topologies. Considering the effect of noise and Markovian switching communication topology, a novel leader-following group formation control protocol with an actuator fault for a multi-AUV system is developed under the influence of the two independent stochastic processes. The designed controller is proved by an infinitesimal generator with Lyapunov stability theory and can guarantee that the follower AUVs’ states will eventually converge to the leader’s state in each subgroup while forming the desired sub-formation. Finally, the effectiveness of the theoretical analysis is verified by a simulation experiment.

Consensus of NMASs with MSTs subjected to DoS attacks under event-triggered control

The leader-following consensus (LFCs) of nonlinear multi-agent systems (NMASs) with Markov switching topologies (MSTs) subjected to denial-of-service (DoS) attacks under event-triggered (ET) control is studied. An ET strategy is applied to reduce unnecessary signal transmission among agents, save network resources, and ensure systems performance. As a result of the open communication network among agents, it is inevitably subjected to attacks that leads to changing in the communication topologies. The communication topologies among agents are modeled as MSTs, and the transfer rates (TRs) are assumed to be partially unknown. DoS attacks are the most common attacks due to their destructive, stealthy, and easy implementation, so the network attacks considered in this paper are DoS attacks. Based on the distributed control theory and Lyapunov stability theory, the Lyapunov direct method and stochastic analysis method are used to explore sufficient conditions for the systems to achieve LFCs. Finally, an example is provided to verify the effectiveness of the methods and the correctness of the results.

Average consensus stability analysis for stochastic multi-agent systems with compound noises under Markovian switching topologies

Average consensus stability analysis for stochastic multi-agent systems with compound noises under Markovian switching topologies

Leader-Following Consensus of Discrete-Time Stochastic Nonlinear Multiagent Systems Under Fixed and Switching Topologies via Impulsive Control

In this article, the leader-following consensus of discrete-time second-order stochastic nonlinear multiagent systems with Markovian switching topology is investigated. Assume that the switching rule between the communication topologies is subject to the average dwell time (ADT) constraint. By taking advantage of the impulsive control strategy, the leader-following consensus issue is transformed into the stability problem of the impulsive error systems. Several sufficient conditions respecting the exponential mean-square stability for impulsive error system under fixed and switching topologies are derived by utilizing the Lyapunov function and the notions of average impulsive interval and ADT. Intriguingly, this article considers that impulsive instant and switching instant are independent of each other. Four potential cases of system evolution under Markovian switching topology are discussed. Finally, simulation results are reported to illustrate the effectiveness of our developed results.

Mean square leader‐following consensus of heterogeneous multi‐agent systems with Markovian switching topologies and communication delays

AbstractThis article considers the mean square leader‐following output consensus problem of heterogeneous multi‐agent systems under randomly switching topologies and time‐varying communication delays. By modeling the switching topologies as a time‐homogeneous Markov process and taking the communication delays into consideration, a distributed observer is proposed to estimate the state of the leader. A novel distributed output feedback controller is then designed. By constructing a novel switching Lyapunov functional, an easily‐verifiable sufficient condition to achieve the mean square leader‐following output consensus is given. Finally, two simulation examples are presented to show the effectiveness of the proposed control scheme.

Switching pinning control for memristive neural networks system with Markovian switching topologies

This work concentrates on the issue of leader-following bipartite synchronization of multiple memristive neural networks with Markovian jump topology. In contrast to conventional coupled neural network systems, the coupled neural network model under consideration possesses both cooperative and competitive connections among neuron nodes. Specifically, the interaction between neighbors’ nodes is described by a signed graph, in which a positive weight represents an alliance relationship between two neuron nodes while a negative weight represents an adversarial relationship between two neuron nodes. By designing a pinning discontinuous controller that makes full use of the mode information, some effective criteria that ensure the stability of bipartite synchronization error states are obtained. All network nodes can synchronize the target node state bipartitely. Finally, two simulation examples are provided to demonstrate the viability of the suggested bipartite synchronization control approach.

Dynamic event-triggered synchronization of complex networks with switching topologies: Asynchronous observer-based case

In this paper, the issue of observer-based synchronization for discrete complex networks with Markov switching topologies is investigated. First, the asynchronous phenomenon between the observer and the node is considered. By resorting to a hidden Markov model (HMM), an non-homogenous observer with an asynchronous topological structure and gain is developed to estimate the state of nodes. Second, for saving precious communication resources, the remote controller updates the control signal based on a dynamic event-triggered scheme (DETS). In this scheme, the threshold of DETS is improved into a diagonal threshold matrix, and the desired system performance can be obtained by flexibly arranging each entry of threshold matrix. To unify the works of the synchronization and state observation, an augmented error system (AES) is established. Subsequently, sufficient conditions for H∞ synchronization of complex networks with asynchronous constraints are proposed by choosing a suitable Lyapunov function. Finally, two simulation examples are implemented to demonstrate the effectiveness of the above results.

Cooperative output feedback consensus control of second-order nonlinear multi-agent systems under Markovian switching topologies

This paper deals with the leader-following consensus problem for a class of second-order nonlinear multi-agent systems by output feedback. The communication topology is characterized by a Markovian switching graph. Firstly, an input-driven observer is introduced to estimate the consensus error of each follower agent. Then, a cooperative nonlinear control law is constructed using the relative output information between neighboring agents by employing the backstepping methodology, which achieves leader-following consensus in mean square sense. Compared with the existing results, the nonlinear functions are required to satisfy polynomial growth condition rather than globally Lipschitz growth or Lipschitz-like growth condition. A numerical example is given to illustrate the theoretical results.

Event-Triggered Bipartite Consensus for Fuzzy Multiagent Systems Under Markovian Switching Signed Topology

In this article, we study the problems of bipartite and cooperative consensus with a strictly dissipative performance for fuzzy multiagent systems (MASs) in a unified framework. First, we prove that bipartite consensus over a structurally balanced signed graph is equivalent to cooperative consensus over the corresponding unsigned graph by leveraging the gauge transformation for a class of nonlinear MASs. Then, a polynomial fuzzy model is constructed to describe the nonlinear MAS formed by one leader and followers. For mitigating communication and computational load, a mode-dependent event-triggered transmission strategy is proposed. By establishing the switching topologies through Markovian process, a new sampled-data event-triggered consensus protocol is designed. With a mode-dependent Lyapunov–Krasovskii function, a novel relaxed dissipative criterion is obtained. The criterion guarantees that all agents can achieve both event-triggered cooperative consensus and event-triggered bipartite consensus with the same magnitude but opposite signs for MASs over structurally balanced signed directed graphs and Markovian switching topologies. Moreover, the event-triggered parameters and consensus control gains can be numerically solved via the sum-of-squares method. Simulation results are given to show the effectiveness of the proposed design method.

Dynamic event-triggered resilient state estimation for time-varying complex networks with Markovian switching topologies

This paper addresses a resilient state estimation problem for an array of nonlinear complex networks with switching topologies under the dynamic event-triggered mechanism (ETM). To reduce the unnecessary data delivery, the dynamic ETM is introduced to schedule the data delivery from sensors to estimators. The model of the switched complex networks is established by adopting a Markov chain which is better to reflect the characteristics of practical complex networks. A set of novel estimators is obtained by using the properties of Kronecker product combining with the Lyapunov–Krasovskii method, and some easy-to-check conditions are derived such that the dynamics of state estimation error satisfies the prescribed H∞ performance index. In addition, the parameters of the designed resilient state estimators can be acquired by solving a series of convex optimization problems. In the end, a simulation example is given to demonstrate the validity of the proposed theoretical results in this paper.

A distributed optimization algorithm over Markov switching topology under adversarial attack

This paper investigates the distributed optimization problem with adversarial agents over Markov switching topology. A Push-DIGing type algorithm is applied to find optimizer of the distributed optimization problem. Different from most existing results on distributed optimization problems with adversary agents, we mainly focus on seeking a fixed step size algorithm under Markov switching communication graph. We first divide the agents into three sets, namely the trust agent set, the normal agent set, and the adversarial agent set. All normal agents only use the state of non-attacked agents for iterations. A practical method is presented to distinguish the adversary agents. It is shown that the states of the trust and normal agents will synchronize to the optimizer with a bounded error if (1) the step size does not exceed an upper bound, (2) the union of the communication graph has a spanning tree, and (3) the differential of a local function is decreasing. Furthermore, we also present the upper and lower bounds on distances between the converged state and the optimizer. An example is presented to verify the effectiveness of our algorithm.

Observer‐based guaranteed cost control for IT‐2 stochastic fuzzy coupled neural networks with Markov switching topology

SummaryThis study focuses on the guaranteed cost control problem for interval type‐2 stochastic fuzzy coupled neural networks (NNs) elicited by the observer framework with Markov switching topology, external disturbances, and quantization effect. In particular, the guaranteed cost controller is developed with an upper bound of the guaranteed cost function and also ensures stability of the addressed networks. Also, the integration of lower and upper membership functions are incorporated to relax the stability condition of the networks. Notably, the randomness phenomena are incorporated by the agency of stochastic variables that satisfies the Bernoulli distribution characteristics. Specifically, the state feedback controller considered with quantization effect is designed through undirected communication graph subject to Markov switching topology. In consequence with Lyapunov–Krasovskii‐functional and algebraic graph theory, sufficient conditions are established to assure the stochastic stabilization of the NNs with some specified cost value. Explicitly, the optimal upper bound of the guaranteed cost function and the controller gain fluctuations of the state and the observer are effectuated through the developed conditions. Finally, the reduced conservatism and efficiency of the proposed analytical design are demonstrated through a numerical example.

Optimal consensus model-free control for multi-agent systems subject to input delays and switching topologies

In this paper, the optimal consensus control problem of the discrete-time multi-agent systems with switching topologies and input delays is investigated by adopting the adaptive dynamic programming method. Through introducing a new state variable, the original input-delayed system can be transformed into a delay-free one. Then, a novel local performance index function is designed for each agent to eliminate the impact of switching topologies, which does not explicitly rely on the information of neighbors. Based on Bellman optimality principle, Lyapunov stability theorem and deep reinforcement learning method, the stability of the error system and the optimality of the value function are proved. In order to solve the consensus problem of the unknown systems, we propose a new value iteration algorithm based on the input and output data of the system, which can not only guarantee the achievement of consensus but also minimize the performance index function. Finally, two numerical simulations based on actor-critic neural networks are given, including the following two cases: periodic switching topologies and Markov switching topologies, to verify the effectiveness of the proposed optimal control scheme.

Mean Square Consensus of General Linear Multiagent Systems with Communication Noises under Switching Topologies

This paper investigates the distributed consensus problem of general linear multiagent systems (MASs) with communication noises under fixed and Markovian switching topologies, respectively. Each agent can obtain full state of itself and receive its neighbors’ state with noises, where intensities of noises are vector functions of relative states of agents. Bearing in mind the above constrains, a consensus protocol is proposed, where the gain matrix is obtained by the algebraic Riccati equation and the coupling strength is restricted in a given interval. By using the stochastic stability theorem, we show that mean square consensus is achieved in fixed topology case and switching topologies case, respectively. Furthermore, an estimation of the exponential convergence rate of consensus is given explicitly. Finally, simulation examples are given to show the correctness of the proposed results.

Consensus stability analysis for stochastic multi-agent systems with multiplicative measurement noises and Markovian switching topologies

<p style='text-indent:20px;'>We investigate the consensus stability for linear stochastic multi-agent systems with multiplicative noises and Markovian random graphs and investigate the asymptotic consensus in the mean square sense for the systems. To establish the consensus stability for the systems, we analysis the consensus error systems by developing general stochastic differential equation with jumps, matrix theory and algebraic graph theory, and then show that the error consensus in the mean square sense finally tending to zero as time goes on is determined by the strongly connected property of union of topologies. Finally, we provide an example to demonstrate the effectiveness of our theoretical results.</p>

Multi-leader-follower group consensus of stochastic time-delay multi-agent systems subject to Markov switching topology.

The multi-leader-follower group consensus issue of a class of stochastic time-delay multi-agent systems subject to Markov switching topology is investigated. The purpose is to determine a distributed control protocol to make sure that the followers' states converge in mean square to a convex hull generated by the leaders' states. Through a model transformation, the problem is transformed into a mean-square stability issue of a new system. Then, an easy-to-check sufficient condition for the solvability of the multi-leader-follower group consensus issue is proposed by utilizing the Lyapunov stability theory, graph theory, as well as several inequality techniques. It is shown that the required feedback gain can be acquired once the condition is satisfied. Finally, an example is used to illustrate the effectiveness of the control protocol.

Multi-group consensus for heterogeneous agents in cooperative–competitive networks via pinning and adaptive coupling weight methods

This paper investigates the multi-group consensus problem for heterogeneous networks via pinning control and adaptive coupling weight methods. In view of the network's topology with connected components, the cooperative–competitive interactions among the agents and Markov switching topology are considered. Based on Lyapunov stability theory and algebraic graph theory, several sufficient conditions and pinning control strategies are presented to guarantee the network reach multi-group consensus. The results reveal that the in-degree of the agents and pinning gains of the second-order agents are closely related to the achievement of multi-group consensus. Finally, simulation experiments are given to verify the correctness of the theoretical results. Moreover, the simulated results show that the adaptive coupling weight method can increase the convergence rate of the network.