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.