Neural Network Boundary Approximation for Uncertain Nonlinear Spatiotemporal Systems and Its Application of Tracking Control.

Abstract

This brief addresses the neural network (NN) approximation problem for uncertain nonlinear systems with time-varying parameters (that is, unknown nonlinear spatiotemporal systems). Due to the fact that the unknown spatiotemporal functions cannot be directly approximated by NNs, a so-called time-varying parameter extraction is given to separate time-varying parameters from uncertain nonlinear spatiotemporal functions. By using the supremum of Euler norm of the extracted time-varying parameters, the nonlinear spatiotemporal function is mapped to an unknown state-based boundary function, which can be approximated by NNs. Based on the time-varying parameter extraction, an adaptive neural tracking control law is designed for uncertain strict-feedback nonlinear spatiotemporal systems, which guarantees the convergence of the tracking error with a trajectory performance. The effectiveness of the designed method is verified by simulations.