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

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.