PID Control of Nonlinear Stochastic Systems with Structural Uncertainties

Abstract

It is widely known that the classical PID (proportional-integral-derivative) controller still plays a dominating role in engineering control systems, and that most of the theoretical studies on PID control focus on linear deterministic systems. In this paper, we will extend the authors recent theoretical investigation by considering additional uncertainties in the input channel, and try to establish a theoretical foundation on the PID control for a class of high-dimensional nonlinear stochastic systems with structural uncertainties consisting of dynamics uncertainty, diffusion uncertainty and input channel uncertainty. We will construct a three dimensional parameter set based on the available information, so that under the classical PID control, the closed-loop control system can be globally stabilized with regulation error tending to zero in the mean square sense, as long as the three PID parameters are chosen from this set. We will further show that global stabilization and asymptotic regulation of a class of multi-agent uncertain nonlinear stochastic systems can also be achieved by uncoupled PID controllers of the agents.