Neural network adaptive control for nonlinear uncertain dynamical systems with asymptotic stability guarantees

Abstract

A neuro adaptive control framework for nonlinear uncertain dynamical systems with input-to-state stable internal dynamics is developed. The proposed framework is Lyapunov-based and unlike standard neural network controllers guaranteeing ultimate boundedness, the framework guarantees partial asymptotic stability of the closed-loop system, that is, asymptotic stability with respect to part of the closed-loop system states associated with the system plant states. The neuro adaptive controllers are constructed without requiring explicit knowledge of the system dynamics other than the assumption that the plant dynamics are continuously differentiable and that the approximation error of uncertain system nonlinearities lie in a small gain-type norm bounded conic sector. This allows us to merge robust control synthesis tools with neural network adaptive control tools to guarantee system stability. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.