Uncoupled PID Control of Multi-Agent Nonlinear Uncertain Stochastic Systems

Abstract

This paper proposes a PID (proportional-integral-derivative) control design method to solve the regulation problem for a class of coupled multi-agent nonlinear uncertain stochastic systems, where each agent only has access to its own regulation error without communicating with others. A three-dimensional manifold will be constructed based on the information about the Lipschitz constants of both the unknown nonlinear drift and diffusion terms, such that the three parameters of each agent’s PID controller can be chosen arbitrarily from this common manifold. It will be shown that such an uncoupled PID design method can globally stabilize the whole nonlinear uncertain stochastic multi-agent system with the regulation error of each agent approaching to zero asymptotically.