Cooperative Control of Multiple Nonlinear Benchmark Systems Perturbed by Second-Order Moment Processes

This paper studies the cooperative control problem of multiple nonlinear benchmark systems perturbed by second-order moment processes. The nonlinear benchmark system consists of a moving car and a rolling ball in oscillating surroundings. When the leader is only accessible to a small part of the followers in a directed graph, a new vectorial backstepping method is proposed for the design of distributed cooperative control laws. By using stochastic analysis techniques and algebra graph theory, it is shown that the cooperative control problem under consideration is solvable. Specifically, the errors between the followers' outputs and the leader's output can be made arbitrarily small while keeping all states of the closed-loop system bounded in probability. Finally, the effectiveness of the proposed control scheme is demonstrated through a simulation example.