Evolutionary optimisation of Hénon map control: A black box approach

Abstract

This paper deals with the usage of heuristics for the optimisation of the control of chaotic system. The main aim of this paper is to show a new approach of solving this problem and constructing new cost functions (CFs) operating in 'black box mode' without a previous exact mathematical analysis of the system, thus without knowledge of the stabilising target state. Three proposals of 'black box' mode CFs were tested in this paper. As a model of deterministic chaotic system, the two-dimensional Hénon map was used. The optimisations were realised in several ways, each one for another desired state of system. Evolutionary algorithms (EAs) self-organising migrating algorithm and differential evolution were used. For each version, repeated simulations were conducted to outline the effectiveness and robustness of the used method and CF. © 2012 Inderscience Enterprises Ltd.