Consensus in multi-agent system with communication constraints based on asynchronous dynamics

Abstract

The consensus in a multi-agent system (MAS) in which each agent communicates with the others over a wireless network is investigated. For the convenience of calculation, analysis and discussion, the MAS under fixed communication topology with communication constraints including random time delay, packet loss and environmental noise is transformed into an asynchronous dynamical system. Thus, the consensus control of the MAS is equivalent to the $H_{\infty }$ control of an asynchronous dynamical system. The sufficient conditions of robust exponential stability of the MAS with communication constraints are proposed and the corresponding $\gamma$ -suboptimal $H_{\infty }$ consensus controllers are designed in terms of linear matrix inequalities (LMIs). The admissible packet loss probability guaranteeing the robust exponential stability of system is also obtained. Subsequently, the corresponding simulation results are provided to demonstrate the effectiveness of the algorithms, and the impacts of time delay and packet loss on consensus of system are analysed in detail.