Evolutionary blackbox control of Logistic equation

This research deals with optimization of the control of chaos by means of evolutionary algorithms. The main aim of this work is to show that evolutionary algorithms are capable of the optimization of chaos control and to show a new approach of solving this problem and constructing new cost functions operating in “blackbox mode” without previous exact mathematical analysis of the system, thus without knowledge of stabilizing target state. Three different cost functions are presented and tested here. As a model of deterministic chaotic system, the one dimensional Logistic equation was used. The optimizations were realized in several ways, each one for another desired periodic orbit. The evolutionary algorithm Self-Organizing Migrating Algorithm (SOMA) was used in four versions. For each version, repeated simulations were conducted to outline the effectiveness and robustness of used method and cost function. Presented results lend weight to the argument, that proposed CFs gives satisfactory results.