Stochastic Switching Topologies Research Articles

Leader-following consensus of data-sampled multi-agent systems with stochastic switching topologies

This paper investigates the leader-following consensus problem for multi-agent systems with Markovian switching topologies in a sampled-data setting. We study two algorithms corresponding to the case where the leader׳s state is time varying or time invariant. With a time-varying leader׳s state, we present necessary and sufficient conditions for boundedness of the tracking error systems. With a time-invariant leader׳s state, we present necessary and sufficient conditions for mean-square stability of the tracking error systems. An optimization algorithm is given to derive the allowable control gains or the feasible sampling period. Simulation examples are presented to show the usefulness of the results.

Consensus in Markovian jump second‐order multi‐agent systems with random communication delay

In this study, the consensus problem for a class of second-order multi-agent systems (MASs) with Markovian characterisations is investigated. The stochastic switching topology and the random communication delay are dominated by two mutually independent Markov chains. The communication delay exists in the switching signal as well as the position information exchanges in the authors’ work. A novel consensus protocol is presented without using the neighbours’ velocity information. By performing three steps of model transformation and introducing a mapping for the two independent Markov chains, the original system is converted into an expanded analogous error system with two Markovian jumping parameters. A necessary and sufficient criterion for the mean square consensus of the Markovian jump second-order MASs with random communication delay is derived. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the theoretical result.

Distributed tracking control of second-order multi-agent systems with sampled data

This paper studies the leader–follower consensus problem of second-order multi-agent dynamical systems with fixed and stochastic switching topologies in a sampled-data setting. A distributed linear consensus protocol is designed to track an active leader, where the current position information of neighbor agents and self-velocity data are utilized. A necessary and sufficient condition is established under fixed and directed topology for reaching consensus, which depends on the sampling period and control gain parameters. A sufficient condition is obtained under the Markov switching topology case. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results.

Group consensus of discrete-time multi-agent systems with fixed and stochastic switching topologies

This paper investigates the group consensus problem for discrete-time multi-agent systems with a fixed topology and stochastic switching topologies. The stochastic switching topologies are assumed to be governed by a finite-time Markov chain. The group consensus problem of the multi-agent systems is converted into the stability problem of the error systems by a model transformation. Based on matrix theory and linear system theory, we obtain two necessary and sufficient conditions of couple-group consensus for the case of fixed topology, and one necessary and sufficient condition of mean-square couple-group consensus for the case of stochastic switching topologies. Algorithms are provided to design the feasible control gains. Then, the results are extended to the case of multi-group consensus. Finally, simulation examples are given to show the effectiveness of the proposed results.

Distributed output feedback consensus of discrete-time multi-agent systems

This paper investigates the problem of distributed output feedback consensus for multi-agent systems. Both fixed topology and stochastic switching topology are considered. It is assumed that each agent updates its state according to the output information of itself and its neighbors. We obtain some necessary and sufficient conditions of consensusability based on algebraic graph theory and Markov jump linear system theory. Algorithms are given to derive the allowable control gains. Simulation results are presented to show the effectiveness of the theoretical results.

Couple-group consensus for second-order multi-agent systems with fixed and stochastic switching topologies

This paper deals with the couple-group consensus problem for second-order discrete-time multi-agent systems. Both the fixed topology case and the stochastic switching topology case are considered. The couple-group consensus problem is converted into the stability problem of the error system by a linear transformation. For the fixed topology case, we obtain two different conditions of couple-group consensus. For the stochastic switching topology case, we obtain a necessary and sufficient condition of mean-square couple-group consensus. Algorithms are provided to design the allowable control gains. Finally, simulation examples are given to show the usefulness of the theoretical results.

Leader-Following Consensus of Multiagent Systems with Time-Varying Delays via Impulsive Control

The leader-following consensus problem for delayed multiagent systems is investigated over stochastic switching topologies via impulsive control method. A distributed consensus protocol is proposed based on sample data information. The convergence analysis for such algorithm over undirected and directed networks is provided, and some sufficient conditions to guarantee the consensus are also established. It is shown that delayed networks can achieve consensus even information is exchanged among followers just at some discrete moments. At last, some numerical examples are given to illustrate the effectiveness of the proposed protocols.

Formation control of multi‐agent systems with stochastic switching topology and time‐varying communication delays

In this study, the authors formulate and study the distributed formation problem of multi-agent systems (MASs) with randomly switching topologies and time-varying delays. The non-linear dynamics of each agent at different time intervals corresponds to different switching mode, and the switching design reflects the changing of travelling path in practical systems. The communication topology of the system switches among finite modes that are governed by a finite-state Markov process. On the basis of artificial potential functions, a formation controller is designed in a general form. Sufficient conditions for stochastic formation stability of the MAS are obtained in terms of a Lyapunov functional and linear matrix inequalities. Some heuristic rules to design a formation controller for the MAS are then presented. Finally, specific potential functions are discussed and corresponding simulation results are provided to demonstrate the effectiveness of the proposed approach.

Consensus problem of networked multi-agent systems with constant communication delay: stochastic switching topology case

This article proposes an observer-based control strategy for networked multi-agent systems with constant communication delay and stochastic switching topology. First, using the system transformation method, the mean-square consensus problem of multi-agent systems can be converted into the mean-square stability problem of an equivalent system, and some equivalent conditions concerning the mean-square consensus are presented. Then, an example is given to illustrate that the connection weights should be regarded as the parameters to be designed, since they have a great effect on the mean-square consensus of multi-agent systems. By choosing appropriate connection weights, the mean-square consensus problem can be converted into the mean-square stabilisation problem of N-1 delay systems with stochastic switching signal, whose related observer-based stabilisability criteria can be established in the form of linear matrix inequalities (LMIs). Furthermore, if the LMIs are feasible, the multi-agent systems achieve mean-square consensus if and only if the union of graphs in the switching topology set has a directed spanning tree. Finally, numerical simulations are given to illustrate our results.

Impulsive consensus seeking in directed networks of multi-agent systems with communication time delays

In this article, we consider average consensus problem in directed delayed networked multi-agent systems having impulsive effects with fixed topology and stochastic switching topology. A simple impulsive consensus protocol for such networks is proposed, and some generic criteria for solving the average consensus problem are analytically derived. It is shown that a directed delayed networked multi-agent system can achieve average consensus globally exponentially with suitable impulsive gain and impulsive interval. Subsequently, two typical illustrative examples, along with computer simulation results, are provided to visualise the effectiveness and feasibility of our theoretical results.

Consentability and protocol design of multi-agent systems with stochastic switching topology

This paper studies the mean square consentability problem for a network of double-integrator agents with stochastic switching topology. It is proved that in Markov-switching topologies, the network is mean square consentable under linear consensus protocol if and only if the union of graphs in the switching topology set has globally reachable nodes. A necessary and sufficient condition of the mean square consensus is obtained. Finally, an LMI approach to the design of the consensus protocol is presented. Numerical simulations are given to illustrate the results.