Abstract
This research deals with the optimization of control of Hénon Map, which is a discrete chaotic system. This work introduces and compares evolutionary approach representing tuning of parameters for an existing control method either with the standard cost function using the numerical desired state as the one of the input or blackbox type cost function, as well as meta-evolutionary approach representing synthesis of a whole control law by means of Analytic Programming (AP). These three approaches are used for the purpose of stabilization of the stable state and higher periodic orbits, which stand for oscillations between several values of chaotic system. For experimentation, Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE) were used.
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References
Zelinka, I., Senkerik, R., Navratil, E.: Investigation on evolutionary optimization of chaos control. Chaos, Solitons & Fractals 40(1), 111–129 (2009)
Senkerik, R., Zelinka, I., Davendra, D., Oplatkova, Z.: Evolutionary Design of Chaos Control in 1D. In: Zelinka, I., Celikovsky, S., Richter, H., Chen, G. (eds.) Evolutionary Algorithms and Chaotic Systems. SCI, vol. 267, pp. 165–190. Springer, Heidelberg (2010)
Senkerik, R., Zelinka, I., Davendra, D., Oplatkova, Z.: Utilization of SOMA and differential evolution for robust stabilization of chaotic Logistic equation. Computers & Mathematics with Applications 60(4), 1026–1037 (2010)
Pyragas, K.: Control of chaos via extended delay feedback. Physics Letters A 206, 323–330 (1995)
Just, W.: Principles of Time Delayed Feedback Control. In: Schuster, H.G. (ed.) Handbook of Chaos Control, Wiley-Vch (1999)
Pyragas, K.: Continuous control of chaos by self-controlling feedback. Physics Letters A 170, 421–428 (1992)
Zelinka, I., Davendra, D., Senkerik, R., Jasek, R., Oplatkova, Z.: Analytical Programming - a Novel Approach for Evolutionary Synthesis of Symbolic Structures. In: Kita, E. (ed.) Evolutionary Algorithms. InTech (2011)
Senkerik, R., Zelinka, I.: Evolutionary Optimization of Chaos Control - A New Approach. In: Proceedings of the 22nd European Conference on Modelling and Simulation, ECMS 2008, Nicosia, pp. 218–223 (2008)
Senkerik, R., Oplatkova, Z., Zelinka, I., Davendra, D.: Synthesis of feedback controller for three selected chaotic systems by means of evolutionary techniques: Analytic programming. Mathematical and Computer Modelling (2010), doi:10.1016/j.mcm.2011.05.030
Senkerik, R., Oplatkova, Z., Zelinka, I., Davendra, D., Jasek, R.: Evolutionary Synthesis of Control Law for Higher Periodic Orbits of Chaotic Logistic Equation. In: 25th European Conference on Modelling and Simulation. European Council for Modelling and Simulation, pp. 452–458 (2011)
Senkerik, R., Oplatkova, Z., Zelinka, I., Davendra, D., Jasek, R.: Synthesis of Feedback Control Law for Stabilization of Chaotic System Oscillations by means of Analytic Programming – Preliminary Study. In: 5th Global Conference on Power Control and Optimization – PCO 2011 (2011)
Zelinka, I., Oplatkova, Z., Nolle, L.: Boolean Symmetry Function Synthesis by Means of Arbitrary Evolutionary Algorithms-Comparative Study. International Journal of Simulation Systems, Science and Technology 6(9), 44–56 (2005) ISSN: 1473-8031
Lampinen, J., Zelinka, I.: New Ideas in Optimization – Mechanical Engineering Design Optimization by Differential Devolution, vol. 1, 20 p. McGraw-hill, London (1999) ISBN 007-709506-5
Oplatková, Z., Zelinka, I.: Investigation on Evolutionary Synthesis of Movement Commands. Modelling and Simulation in Engineering 2009, Article ID 845080, 12 pages (2009) ISSN: 1687-559
Hilborn, R.C.: Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers. Oxford University Press (2000)
Zelinka, I.: SOMA – Self Organizing Migrating Algorithm. In: Babu, B.V., Onwubolu, G. (eds.) New Optimization Techniques in Engineering, vol. 33, ch. 7. Springer (2004)
Price, K., Storn, R.M., Lampinen, J.A.: Differential Evolution: A Practical Approach to Global Optimization. Natural Computing Series. Springer (1995)
Coelho, L.D.: Self-organizing migration algorithm applied to machining allocation of clutch assembly. Mathematics and Computers in Simulation 80(2), 427–435 (2009)
Coelho, L.D.: Self-Organizing Migrating Strategies Applied to Reliability-Redundancy Optimization of Systems. IEEE Transactions on Reliability 58(3), 501–510 (2009)
Coelho, L.D., Mariani, V.C.: An efficient cultural self-organizing migrating strategy for economic dispatch optimization with valve-point effect. Energy Conversion and Management 51(12), 2580–2587 (2010)
Davendra, D., Zelinka, I., Senkerik, R.: Chaos driven evolutionary algorithms for the task of PID control. Computers & Mathematics with Applications 60(4), 1088–1104 (2010)
Matousek, R.: GAHC: Improved GA with HC station. In: Proceedings of WCECS 2007, San Francisco, pp. 915–920 (2007)
Matousek, R.: HC12: The Principle of CUDA Implementation. In: Proceedings of MENDEL 2010. Mendel Journal series, pp. 303–308 (2010) ISSN: 1803-3814
Zelinka, I.: SOMA homepage, http://www.fai.utb.cz/people/zelinka/soma/ (accessed September 30, 2011)
Price, K., Storn, R.M.: Differential evolution home-page (2001), http://www.icsi.berkeley.edu/~storn/code.html (accessed September 30, 2011)
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Senkerik, R., Oplatkova, Z., Zelinka, I., Davendra, D.D., Jasek, R. (2013). Application of Evolutionary Techniques for Optimization of Chaos Control – Introduction of Three Approaches. In: Zelinka, I., Snášel, V., Abraham, A. (eds) Handbook of Optimization. Intelligent Systems Reference Library, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30504-7_31
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