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Introduction

Lyapunov functions are of fundamental importance in the study of nonlinear systems. Not only are Lyapunov function useful in proving stability of nonlinear systems, they are an important part of certain nonlinear control design methods, including backstepping and sliding mode.

Unfortunately, there are no general methods for finding a Lyapunov function for a given system. In this report, I apply genetic programming, a heuristic optimization technique that is a variation of genetic algorithms where the objective vectors can be complex mathematical expressions, to the general Lyapunov-finding problem.

Genetic programming is a relatively new field, first introduced by Koza in 1992 [1]. Ref. 1 remains the most comprehensive introduction and reference for genetic programming. As yet, there is very little literature on the application of genetic programming to nonlinear dynamics problems. Of the few papers that examine this, most focused on system identification [2] or controller design by searching for a control law [3].

This report first reviews genetic algorithms and genetic programming, before examining the Lyapunov search algorithm.



Carl Banks 2002-05-17