Adaptive dynamic surface control of stochastic nonstrict‐feedback constrained nonlinear systems with input and state unmodeled dynamics

Abstract

SummaryIn this paper, the issue of adaptive neural control is discussed for a class of stochastic nonstrict‐feedback constrained nonlinear systems with input and state unmodeled dynamics. A dynamic signal produced by the first‐order auxiliary system is employed to deal with the dynamical uncertain terms. Radial basis function neural networks are used to reconstruct unknown nonlinear continuous functions. With the help of the mean value theorem and Young's inequality, only one learning parameter is adjusted online at recursive each step. Using the hyperbolic tangent function as nonlinear mapping, the output constrained stochastic nonstrict‐feedback system in the presence of unmodeled dynamics is transformed into a novel unconstrained stochastic nonstrict‐feedback system. Based on dynamic surface control technology and the property of Gaussian function, adaptive neural control is developed for the transformed stochastic nonstrict‐feedback system. The output abides by stochastic constraints in probability. By the Lyapunov method, all signals of the closed‐loop control system are proved to be semi‐global uniform ultimate bounded (SGUUB) in probability. The obtained theoretical findings are verified by two numerical examples.