Utilization of SOMA and differential evolution for robust stabilization of chaotic Logistic equation

Authors:
Roman Senkerik;Ivan Zelinka;Donald Davendra;Zuzana Oplatkova
Affiliations:
Tomas Bata University in Zlin, Department of Applied Informatics, Nad Stranemi 4511, 76005 Zlin, Czech Republic;Tomas Bata University in Zlin, Department of Applied Informatics, Nad Stranemi 4511, 76005 Zlin, Czech Republic;Tomas Bata University in Zlin, Department of Applied Informatics, Nad Stranemi 4511, 76005 Zlin, Czech Republic;Tomas Bata University in Zlin, Department of Applied Informatics, Nad Stranemi 4511, 76005 Zlin, Czech Republic
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

This paper deals with the utilization of two evolutionary algorithms Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE) for the optimization of the control of chaos. This paper is aimed at an explanation on how to use evolutionary algorithms (EAs) and how to properly define the advanced targeting cost function (CF) securing fast, precise and mainly robust stabilization of selected chaotic system on a desired state for any initial conditions. The role of EA here is as a powerful tool for an optimal tuning of control technique input parameters. As a model of deterministic chaotic system, the one-dimensional discrete Logistic equation was used. The four canonical strategies of SOMA and six canonical strategies of DE were utilized. For each EA strategy, repeated simulations were conducted to outline the effectiveness and robustness of used method and targeting CF securing robust solution. Satisfactory results obtained by both heuristic and the two proposed cost functions are compared with previous research, given by different cost function designs.