Title: Evolutionary optimisation of Hénon map control: a black box approach

Authors: Roman Senkerik; Ivan Zelinka; Donald Davendra; Zuzana Oplatkova

Addresses: Faculty of Applied Informatics, Department of Informatics and Artificial Intelligence, Tomas Bata University in Zlin, Nad Stranemi 4511, Zlin 76005, Czech Republic ' Faculty of Electrical Engineering and Computer Science, Department of Computer Science, VSB – Technical University of Ostrava, 17. listopadu 15, Ostrava-Poruba 708 33, Czech Republic ' Faculty of Applied Informatics, Department of Informatics and Artificial Intelligence, Tomas Bata University in Zlin, Nad Stranemi 4511, Zlin 76005, Czech Republic ' Faculty of Applied Informatics, Department of Informatics and Artificial Intelligence, Tomas Bata University in Zlin, Nad Stranemi 4511, Zlin 76005, Czech Republic

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.

Keywords: optimisation; chaos control; EAs; evolutionary algorithms; differential evolution; SOMA; self-organising migrating algorithm; heuristics; simulation.

DOI: 10.1504/IJOR.2012.045183

International Journal of Operational Research, 2012 Vol.13 No.2, pp.129 - 146

Available online: 27 Jan 2012 *

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