Robust Consensus Of Multi-Agent Systems

Recently consensus problems of network multi-agent systems have attracted many researchers’attention and are widely applied in different fields, such as biology, mathematics,computer and control community. The key to the consensus problem is that how to design a suitable protocol make all agents reach agreement. Most existing papers are assumed that multi-agent systems work in an ideal environment. In the real circumstances, information communication between interaction agents of networks may suffer form communication delays and measurement noises, each agent can not receive its neighbours’information accurately, which may lead to the instability of a multi-agent system. Therefore it is of great significance for consensus of multi-agent systems in a complex environment.This paper is studied the robust consensus problem of a discrete-time first-order multi-agent system in a complex environment(noises/delays) on general directed unbalanced networks under fixed topologies or switching topologies. This paper mainly includes the following two aspects:1.Robust consensus of multi-agent systems with communication noises and communication delays under fixed topology. There are many excellent works about consensus problem of multi-agent systems in literature. The time delays and communication noises are taken into consideration in this paper based on the consensus problem. We proved that as long as the communication delays are bounded,the state of every agent converges to a random variable. Finally, the simulation example proves the main conclusion of this article.2.Robust consensus of multi-agent systems with communication noises and communication delays under switching topologies.Owing to the presence of communication noises and delays, existing techniques such as the stochastic Lyapunov theory are no longer applicable to the analysis of consensus. Consider the network is a switching topology and directed unbalanced graph,the consensus problem for multi-agent systems with noises and delays are studied.The introduction of time-varying control gain is to attenuate noise,the consensus problem with time delays is converted to the consensus problem without delays by model transformation. We propose consensus protocols that take the noisy measurements and the communication time-delays into account, and prove mean square consensus for switching directed multi-agent systems by using the state augmentation technique and the property of the transition matrix.In short, under fixed topology or switching topologies as well as the influence of time delays and measurement noises, the algorithm is convergent, and can achieve mean square consensus.