Synthesis of feedback controller for stabilization of chaotic Hénon Map oscillations by means of analytic programming

Abstract

This research deals with a synthesis of control law by means of analytic programming for selected discrete chaotic system - Hénon Map. The novelty of the approach is that analytic programming as a tool for symbolic regression is used for the purpose of stabilization of higher periodic orbits, which represent the oscillations between several values of chaotic system. The paper consists of the descriptions of analytic programming as well as used chaotic system and detailed proposal of cost function used in optimization process. For experimentation, Self-Organizing Migrating Algorithm (SOMA) with analytic programming and Differential evolution (DE) as second algorithm for meta-evolution were used.