Utilization of analytic programming for the stabilization of high order oscillations of chaotic Hénon map

Proceedings - 26th European Conference on Modelling and Simulation, ECMS 2012

Volumn , Issue , 2012, Pages

  Oplatkova, Zuzana ^a   Senkerik, Roman ^a   Zelinka, Ivan ^b   Davendra, Donald ^b  

^a TOMAS BATA UNIVERSITY IN ZLIN   (Czech Republic)

^b VSB TECHNICAL UNIVERSITY OF OSTRAVA   (Czech Republic)

Author keywords

Analytic programming; Chaos; Control; Differential evolution; Evolutionary computation; H non map; SOMA

Indexed keywords

CHAOS THEORY; CHAOTIC SYSTEMS; CONTROL ENGINEERING; COST FUNCTIONS; EVOLUTIONARY ALGORITHMS; OPTIMIZATION;

ANALYTIC PROGRAMMING; CONTROL LAWS; DIFFERENTIAL EVOLUTION; DISCRETE CHAOTIC SYSTEMS; PERIODIC ORBITS; SELF-ORGANIZING MIGRATING ALGORITHM; SOMA; SYMBOLIC REGRESSION;

STABILIZATION;

EID: 85086494037     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.7148/2012-0410-0416     Document Type: Conference Paper

References (21)

1. Hilborn R.C., 2000. Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, Oxford University Press, 2000, ISBN: 0-19-850723-2.
2. Just W., 1999, "Principles of Time Delayed Feedback Control", In: Schuster H.G., Handbook of Chaos Control, Wiley-Vch, ISBN 3-527-29436-8.
3. Kwon O. J., 1999. "Targeting and Stabilizing Chaotic Trajectories in the Standard Map", Physics Letters A. vol. 258, 1999, pp. 229-236.
4. Lampinen J., Zelinka I., 1999, "New Ideas in Optimization - Mechanical Engineering Design Optimization by Differential Evolution", Volume 1, London: McGraw-hill, 1999, 20 p., ISBN 007-709506-5.
5. Matousek R., 2007, "GAHC: Improved GA with HC station", In WCECS 2007, San Francisco, pp. 915-920. ISBN: 978-988-98671-6-4.
6. Matousek R., 2010, "HC12: The Principle of CUDA Implementation" . In MENDEL 2010, Mendel Journal series, pp. 303-308. ISBN: 978-80-214-4120- 0. ISSN: 1803 3814.
7. Oplatková, Z., Zelinka, I.: 2009. Investigation on Evolutionary Synthesis of Movement Commands, Modelling and Simulation in Engineering, Volume 2009 (2009), Article ID 845080, 12 pages, Hindawi Publishing Corporation, ISSN: 1687-559.
8. Oplatkova Z., Senkerik R., Zelinka I., Holoska J., 2010a, Synthesis of Control Law for Chaotic Henon System - Preliminary study, ECMS 2010, Kuala Lumpur, Malaysia, p. 277-282, ISBN 978-0-9564944-0-5.
9. Oplatkova Z., Senkerik R., Belaskova S., Zelinka I., 2010b, Synthesis of Control Rule for Synthesized Chaotic System by means of Evolutionary Techniques, Mendel 2010, Brno, Czech Republic, p. 91 - 98, ISBN 978-80-214-4120-0.
10. Ott E., C. Greboki, J.A. Yorke, 1990. "Controlling Chaos", Phys. Rev. Lett. vol. 64, 1990, pp. 1196-1199.
11. Price, K. and Storn, R. (2001), Differential evolution homepage, [Online]: http://www.icsi.berkeley.edu/~storn/code.html, [Accessed 29/02/2012].
12. Price K., Storn R. M., Lampinen J. A., 2005, "Differential Evolution : A Practical Approach to Global Optimization", (Natural Computing Series), Springer; 1 edition.
13. Pyragas K., 1992, "Continuous control of chaos by selfcontrolling feedback", Physics Letters A, 170, 421-428.
14. Pyragas K., 1995. "Control of chaos via extended delay feedback", Physics Letters A, vol. 206, 1995, pp. 323-330.
15. Senkerik R., Zelinka I., Navratil E., 2006, "Optimization of feedback control of chaos by evolutionary algorithms", in proc 1st IFAC Conference on analysis and control of chaotic systems, Reims, France, pp. 97 - 102.
16. Senkerik R., Zelinka I., Davendra D., Oplatkova Z., 2010a, "Utilization of SOMA and differential evolution for robust stabilization of chaotic Logistic equation", Computers & Mathematics with Applications, Volume 60, Issue 4, pp. 1026-1037.
17. Senkerik R., Oplatkova Z., Zelinka I., Davendra D.,Jasek R., 2010b, "Synthesis Of Feedback Controller For Chaotic Systems By Means Of Evolutionary Techniques,", Proceeding of Fourth Global Conference on Power Control and Optimization, Sarawak, Borneo, 2010
18. Zelinka I., 2004. "SOMA - Self Organizing Migrating Algorithm", In: New Optimization Techniques in Engineering, (B.V. Babu, G. Onwubolu (eds)), chapter 7, 33, Springer-Verlag, 2004, ISBN 3-540-20167X.
19. Zelinka I.,Oplatkova Z, Nolle L., 2005. Boolean Symmetry Function Synthesis by Means of Arbitrary Evolutionary Algorithms-Comparative Study, International Journal of Simulation Systems, Science and Technology, Volume 6, Number 9, August 2005, pages 44 - 56, ISSN: 1473-8031.
20. Zelinka I., Senkerik R., Navratil E., 2009, "Investigation on evolutionary optimization of chaos control", Chaos, Solitons & Fractals, Volume 40, Issue 1, pp. 111-129.
21. Zelinka, I., Guanrong Ch., Celikovsky S., 2008. Chaos Synthesis by Means of Evolutionary algorithms, International Journal of Bifurcation and Chaos, Vol. 18, No. 4 (2008) 911-942