A combined NN and dynamic gain-based approach to further stabilize nonlinear time-delay systems

Abstract

This paper focuses on the state-feedback control problem for a class of high-order nonlinear systems with unknown time delay and control coefficients. Based on a novel dynamic gain-based backstepping technique and radial basis function neural network (RBF NN) approximation approach, the restrictions on high-order and nonlinearities are removed or further relaxed. Under these weaker conditions, a smooth state-feedback controller is skillfully constructed with only one adaptive parameter. In addition, the knowledge of time delay, NN nodes and weights is not necessary to be known a priori. It is proven that the designed controller can render the closed-loop system be semi-globally uniformly ultimately bounded. Finally, both practical and numerical examples are shown to demonstrate the effectiveness of the proposed scheme.