Analytic programming in the task of evolutionary synthesis of a controller for high order oscillations stabilization of discrete chaotic systems

Authors:
Zuzana Kominkova Oplatkova;Roman Senkerik;Ivan Zelinka;Michal Pluhacek
Affiliations:
Tomas Bata University in Zlin, Faculty of Applied Informatics, Nam. T.G. Masaryka 5555, 760 01 Zlin, Czech Republic;Tomas Bata University in Zlin, Faculty of Applied Informatics, Nam. T.G. Masaryka 5555, 760 01 Zlin, Czech Republic;VŠB-Technical University of Ostrava, Faculty of Electrical Engineering and Computer Science, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic;Tomas Bata University in Zlin, Faculty of Applied Informatics, Nam. T.G. Masaryka 5555, 760 01 Zlin, Czech Republic
Venue:
Computers & Mathematics with Applications
Year:
2013

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Abstract

This paper deals with the utilization of a symbolic regression tool, which is Analytic Programming (AP), together with two evolutionary algorithms, the Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE), for the synthesis of a new control law. This synthesized chaotic controller secures the stabilization of higher periodic orbits, which represent oscillations between several values of three selected discrete chaotic systems. Selected examples were: an artificially evolutionary synthesized system, logistic equation and Henon map. The paper consists of the description of analytic programming as well as chaotic systems used, evolutionary techniques and the cost function.