Mean Square Consensus Research Articles

Consensus control of multi-agent systems with missing data in actuators and Markovian communication failure

This article investigates the consensus problem of multi-agent systems (MASs) with imperfect communication both in channels and in actuators. The data transmission among agents may fail due to limited communication capacity, and the actuators may fail to receive information owing to noisy environment. We use a Markov chain approach to characterise the occurrence of the two types missing data in a unified framework. A sufficient consensus condition is first obtained in terms of linear matrix inequalities. Then, based on this condition, a novel controller design method is further developed such that the MAS with imperfect communication reaches mean-square consensus. It is shown that the consensus problem for MASs with switching topology can be regarded as a special case of the problem considered in this article, and the related theoretical results are presented as well. Numerical examples are provided to illustrate the effectiveness of the proposed approach.

Consensus of output-coupled high-order linear multi-agent systems under deterministic and Markovian switching networks

Consensus problem for high-order multi-agent systems is considered under deterministic and Markovian switching topologies. Only relative output information of agents is assumed to be available through the networks. First, a necessary and sufficient condition for achieving a consensus under a fixed communication network is presented. Based on this result and the stability of switched systems, a high-order multi-agent system with the proposed low-gain controller is shown to reach a consensus under deterministic switching network if the total time when the network is disconnected is, in some senses, smaller than the total time of the network being connected. Furthermore, the conditions sufficient for a high-order multi-agent system to reach an almost sure and mean-square consensus, under Markovian switching networks, are presented. Finally, illustrative examples are given to demonstrate the results.

Event-Based Control for Average Consensus of Wireless Sensor Networks with Stochastic Communication Noises

This paper focuses on the average consensus problem for the wireless sensor networks (WSNs) with fixed and Markovian switching, undirected and connected network topologies in the noise environment. Event-based protocol is applied to each sensor node to reach the consensus. An event triggering strategy is designed based on a Lyapunov function. Under the event trigger condition, some sufficient conditions for average consensus in mean square are obtained. Finally, some numerical simulations are given to illustrate the effectiveness of the results derived in this paper.

Dynamic Average Consensus and Consensusability of General Linear Multiagent Systems with Random Packet Dropout

This paper is concerned with the consensus problem of general linear discrete-time multiagent systems (MASs) with random packet dropout that happens during information exchange between agents. The packet dropout phenomenon is characterized as being a Bernoulli random process. A distributed consensus protocol with weighted graph is proposed to address the packet dropout phenomenon. Through introducing a new disagreement vector, a new framework is established to solve the consensus problem. Based on the control theory, the perturbation argument, and the matrix theory, the necessary and sufficient condition for MASs to reach mean-square consensus is derived in terms of stability of an array of low-dimensional matrices. Moreover, mean-square consensusable conditions with regard to network topology and agent dynamic structure are also provided. Finally, the effectiveness of the theoretical results is demonstrated through an illustrative example.

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.

Maximum Allowable Loss Probability for Consensus of Multi-Agent Systems Over Random Weighted Lossy Networks

This note studies the consensus seeking problem for a team of general linear dynamical agents that communicate via a weighted random lossy network. Linear state feedback consensus protocols are applied and both the weights and feedback gain are treated as control parameters in the protocol. It is shown that the weights and the link loss probabilities of a network have non-negligible effects on the consensus seeking ability of multi-agent systems. Firstly, a weight condition characterized by the eigenvalues of the weighted Laplacian matrix is given for systems over ideal communication networks without packet losses. Secondly, based on stochastic stability analysis a maximum allowable loss probability bound is proposed for systems over random lossy networks. As long as the link loss probabilities of the network are less than this bound and the mean topology has spanning trees, there exist linear protocols solving the mean-square consensus problem of the system.

Stochastic consensus in directed networks of agents with non-linear dynamics and repairable actuator failures

In this study, the problem of stochastic consensus in multi-agent systems of non-linear dynamical agents with state-dependent noise perturbations and repairable actuator failures is investigated. By appropriately constructing a Lyapunov function and using tools from the stochastic differential equations theory, it is proved that mean-square consensus in the closed-loop multi-agent systems with a fixed strongly connected topology can be achieved exponentially if the coupling strength of relative states among neighbouring agents is larger than a threshold value depending on the actuator failure rate. The convergence rate is also analytically given. The results are then extended to the more general case where the communication topology only contains a directed spanning tree. Numerical simulations are finally provided to illustrate the effectiveness of the theoretical analysis.

Mean Square Consensus Control for Second Order Multi-Agent Systems under Fixed Topologies and Measurement Noises

This paper considers the mean square consensus problems for second order multi-agent systems with fixed topologies and measurement noises. Two cases were analyzed: 1) undirected networks with fixed topologies; 2) undirected networks with fixed topologies and measurement noises. In order to attenuate the measurement noises, a time-varying consensus gain was introduced in the consensus protocol. Sufficient conditions were derived for all agents to reach consensus in mean square via algebraic graph theory, matrix theory and stochastic analysis approach, by constructing an appropriate Lyapunov function. A numerical example was given to verify our theoretical analysis.