Adaptive bounding techniques for stable neural control systems

This paper considers the design of stable adaptive neural controllers for uncertain nonlinear dynamical systems with unknown nonlinearities. The Lyapunov synthesis approach is used to develop state-feedback adaptive control schemes based on a general class of nonlinearly parametrized neural network models. The key assumptions are that the system uncertainty satisfies a “strict-feedback” condition and that the network reconstruction error and higher-order terms (with respect to the parameter estimates) 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 neighborhood of zero tracking error