Chaotic Behaviour in Some Discrete –Time Adaptive Control Systems

Abstract

It has been shown that nonlinear discrete maps can display extremely rich behaviour and under certain parameter conditions to show chaotic phenomenon. This work looks at adaptive control feedback systems which can be represented as nonlinear discrete maps and shows how model mismatch can lead to undesired complicated and chaotic behaviour. Moreover that a discrete-time adaptive control system which can display chaotic behaviour can be extended into higher order systems and the results show that under certain parameter conditions, the higher order systems also behave chaotically. A generalised equation form for the eigenvalues is also given.