Application of analytic programming for evolutionary synthesis of control law-introduction of two approaches

Abstract

This research deals with an evolutionary synthesis of control law for Logistic equation, which is a discrete chaotic system. The novelty of the research is that an Analytic Programming (AP), which is a tool for symbolic regression, is used for the synthesis of feedback controller for chaotic system. This work introduces and compares two approaches representing blackbox type cost function, as well as not-blackbox type cost function. These two approaches are used for the purpose of stabilisation of the higher periodic orbits, which stand for oscillations between several values of chaotic system. The work consists of the descriptions of analytic programming as well as chaotic system and used cost functions. For experimentation, Self-Organising Migrating Algorithm (SOMA) and Differential Evolution (DE) were used. © 2012 Springer Berlin Heidelberg.