Time-varying formation control for heterogeneous multi-agent systems with random network and measurement noise

Abstract

This paper addresses the formation control problem of heterogeneous multi-agent systems (MASs) comprising first-order and second-order agents, where the desired formation can be time-varying. Different from previous works, this paper comprehensively takes into account the impact of measurement noise and random network, enhancing the overall applicability of control protocols. Firstly, the time-varying formation control problem of heterogeneous MASs is transformed into the stability problem of nonautonomous stochastic systems. Then by employing the stochastic Lyapunov function and martingale convergence theorem for stability analysis, the formation conditions in mean square and almost sure for control gains are derived for scenarios with additive and multiplicative noise, respectively. Moreover, the paper provides an explicit expression for the mathematical expectation of the formation center function. This expression effectively characterizes the macroscopic trajectory of the entire time-varying formation, considering the impact of both random network and measurement noise. Finally, numerical simulations show the effectiveness of our theoretical results.