Input-Output Linearization of Nonlinear Dynamical Systems: an Introduction

Abstract

The control concepts presented in the previous chapters addressed the control of systems which contain localized unknown nonlinearities within an otherwise (mainly) known linear structure. In the this part of the book, we will consider the problem of controlling a more general class of nonlinear plants, using considerably less prior knowledge. This is motivated by the capabilities of biological neural “controllers”, which enable humans and animals to control complex nonlinear systems without using any mathematically formulated prior knowledge. However, while the controller itself should use as little mathematical knowledge as possible and acquire the necessary knowledge about the plant by means of a suitable learning law, considerable mathematical background is required to find such a learning law which should guarantee stability and well-defined control performance. In this chapter we will introduce some mathematical tools for the treatment of nonlinear dynamical systems, which will be needed in the following chapter to develop a neural network control concept for a quite general class of nonlinear plants.