Bidirectional Convergence Of Multi - Autonomous Systems With Measurement Noise

Competition and cooperation are two types of common relationships between individuals in multi-agent systems. Concerned about the properties of multi-agent systems with antagonistic interactions, this paper devotes to first-order integral multi-agent systems,which is one kind of the most basic multi-agent systems. Faced to undirected signed graph and directed signed graph cases, the influences of measurement noises on the bipartite consensus of multi-agent systems are studied, and the main conclusions are as follows:1. In the case that the interactions between agents are shaped by undirected signed graph, the bipartite consensus problems of first-order integral multi-agent systems with antagonistic interactions and measurement noises are settled. Firstly, a kind of bipartite consensus protocol is designed. Then, this paper gives sufficient conditions for the control law to be a bipartite consensus protocol and the estimations of the final states of individuals. Particularly, when the noises vanish, the conditions can be sufficient and necessary.2. In the case that the interactions between agents are shaped by directed signed graph, the bipartite consensus problems of first-order integral multi-agent systems with antagonistic interactions and measurement noises are also settled. We give a conception of mean square bipartite consensus protocol and with the help of solution of stochastic differential equation and Cauchy criterion, sufficient conditions and necessary conditions are proposed. When measurement noises vanish, some conditions are verified to be sufficient and necessary for a protocol to be a bipartite consensus protocol. What’s more, the consensus groups are determined.