Resilient control design for consensus of nonlinear multi-agent systems with switching topology and randomly varying communication delays

Abstract

This paper examines the robust consensus problem of nonlinear multi-agent systems via a resilient controller subject to switching topology, wherein the effect of uncertainty in the form of additive perturbations and a randomly varying communication delay is considered in the control design. In particular, a directed graph is used to describe the interaction topology of the addressed multi-agent system and a stochastic variable obeying the Bernoulli distributed white sequences is incorporated to represent the randomness of delay. By utilizing the Lyapunov’s direct method and some matrix operations, a sufficient condition for mean-square asymptotic consensus of the addressed system is derived. Subsequently, the explicit characterization of the resilient control gain is obtained by means of linear matrix inequalities that can be effectively solved by using the ideas of convex optimization. An academic example is eventually presented to illustrate the significance and potency of the proposed control design strategy.