Stable adaptive neural control scheme for nonlinear systems

TLDR

Adaptive neural control schemes based on Lyapunov synthesis have been developed in recent years but have only been applied to simple nonlinear systems. This paper develops a design methodology that expands the class of nonlinear systems amenable to adaptive neural control and relaxes restrictive assumptions. The methodology relaxes the need for a known bound on network reconstruction error and employs a smooth state‑dependent feedback control law. The resulting adaptive scheme guarantees semiglobal uniform ultimate boundedness.

Abstract

Based on the Lyapunov synthesis approach, several adaptive neural control schemes have been developed during the last few years. So far, these schemes have been applied only to simple classes of nonlinear systems. This paper develops a design methodology that expands the class of nonlinear systems that adaptive neural control schemes can be applied to and relaxes some of the restrictive assumptions that are usually made. One such assumption is the requirement of a known bound on the network reconstruction error. The overall adaptive scheme is shown to guarantee semiglobal uniform ultimate boundedness. The proposed feedback control law is a smooth function of the state.