Composite Adaptive Control of Continuous-Time Systems

Abstract

In this chapter we introduce an improved adaptation scheme for control of functional uncertain nonlinear systems by neural networks. The proposed scheme, inspired from the composite adaptation law of Slotine and Li [233] that was originally developed for parametric uncertain systems, aims to improve the transient performance of RBF-based adaptive schemes for continuous time affine, nonlinear systems, such as those found in [204, 219, 255]. Although these papers do provide control and adaptation laws that ensure boundedness of all the system’s signals and tracking error convergence, performance issues such as rate of convergence and general improvements in the transient response are not addressed at all. Indeed this topic has been largely neglected even in the classical literature on linear adaptive control, where not many results abound [144, 182]. The few principal works dealing with this problem in the linear, parametric uncertain case are briefly described next.