PID Control for High Dimensional Nonlinear Uncertain Stochastic Systems

It is widely recognized that the classical proportional-integral-derivative (PIE)) controller plays a fundamental role in the control of industrial processes, and that the easy-to-use simple structure together with the strong robustness of the PID controller demonstrate its supremacy when dealing with real world systems. However, we should admit the fact that almost all the existing studies focus on linear deterministic models, while almost all the practical systems are nonlinear with uncertainties including random noises. This motivates our theoretical study on nonlinear uncertain stochastic systems in this paper. To be specific. we will provide an explicit way to construct the PID parameters based on some knowledge of the upper bounds of the derivatives of both unknown nonlinear drift and diffusion terms. We will also show that the closed-loop system will be globally stable and the second moment of regulation error E parallel to y(t) - y*parallel to(2) tends to zero.