Approximation-based adaptive control

Abstract

This chapter is focused on the design and analysis of adaptive controllers for dynamical systems operating in the presence of nonparametric unknown nonlinear functions and bounded time-varying disturbances. In order to counter these types of uncertainties, we will employ direct adaptive model reference controllers equipped with online function approximation architectures, such as artificial neural networks (NNs). We begin with an introductory review of theoretical results related to function approximation by NNs, (Sects. 12.1, 12.2, and 12.3). As for any other function representation constructs, NN-based approximations are valid only on bounded sets. So, a suitable control design must account for a set of state limiting constraints imposed by the chosen function approximation method. For our proposed adaptive control design (Sect.12.4), we will utilize online tunable artificial NNs to represent unstructured uncertainties in the system dynamics of interest. In addition, we will add a state limiting design modification to keep the system trajectories within predefined NN-induced state limiting constraints. We end this chapter with a comprehensive step-by-step design example of an automatic landing system for a medium-size transport aircraft.