Stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators

TLDR

Stable adaptive neural controllers for uncertain nonlinear dynamical systems with unknown nonlinearities are designed under strict‑feedback and bounded‑error assumptions. A Lyapunov‑based state‑feedback scheme employing nonlinearly parametrized online approximators and an adaptive bounding design ensures semi‑global uniform ultimate boundedness of the tracking error. Theoretical guarantees are illustrated by a simulation example showing the controller achieves the desired bounded tracking performance.

Abstract

The design of stable adaptive neural controllers for uncertain nonlinear dynamical systems with unknown nonlinearities is considered. The Lyapunov synthesis approach is used to develop state-feedback adaptive control schemes based on a general class of nonlinearly parametrized on-line approximation models. The key assumptions are that the system uncertainty satisfies a strict feedback condition and that the network reconstruction error and higher-order terms of the on-line approximator (with respect to the network weights) satisfy certain bounding conditions. An adaptive bounding design is used to show that the overall neural control system guarantees semi-global uniform ultimate boundedness within a neighbourhood of zero tracking error. The theoretical results are illustrated through a simulation example.