Leader-following consensus of linear multi-agent systems with randomly occurring nonlinearities and uncertainties and stochastic disturbances

For the multi-agent community, one of the key challenges is the agents operating in open environments, in which stochastic noises affect the dynamics of agents. This paper deals with the leader-following consensus problem for a class of linear multi-agent systems model with randomly occurring nonlinearities and uncertainties, and stochastic disturbances. The communication topology is assumed to be undirected and fixed. The stochastic Brownian motions are used to describe the source of extrinsic disturbances. The randomly occurring nonlinearities are introduced to describe the nonlinear intrinsic dynamics occurring in a probabilistic way. The randomly occurring uncertainties are adopted to reflect more realistic dynamical behaviors of the agent systems that are caused by noisy environment. Sufficient conditions are derived to make all follower agents asymptotically reach the state of leader in the mean square sense. Simulation results illustrate the theoretical results.