Chaos synthesis by means of evolutionary algorithms

International Journal of Bifurcation and Chaos

Volumn 18, Issue 4, 2008, Pages 911-942

  Zelinka, Ivan ^a   Chen, Guanrong ^b   Celikovsky, Sergej ^c  

^a TOMAS BATA UNIVERSITY IN ZLIN   (Czech Republic)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^c INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

Author keywords

Bifurcation; Chaos; Differential evolution; Evolution; Genetic algorithm; Lyapunov exponent; Optimization; SOMA; Synthesis

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; CHAOTIC SYSTEMS; COST FUNCTIONS; GENETIC ALGORITHMS; GENETIC PROGRAMMING; LYAPUNOV METHODS; OPTIMIZATION; SYNTHESIS (CHEMICAL);

CASE-STUDIES; DIFFERENTIAL EVOLUTION; EVOLUTION; GRAMMATICAL EVOLUTION; LYAPUNOV EXPONENT; RELIABILITY AND ROBUSTNESS; SOMA;

EVOLUTIONARY ALGORITHMS;

EID: 45449087269     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021812740802077X     Document Type: Article

References (60)

1. Alvarez, J., Puebla, H. & Cervantes, I. [2002] "Stability of observer-based chaotic communication for a class of Lur'e systems," Int. J. Bifurcation and Chaos 7, 1605-1618.
2. Back, T., Fogel, D. B. & Michalewicz, Z. [1997] Handbook of Evolutionary Computation (Institute of Physics, London).
3. Beyer, H.-G. [2001] Theory of Evolution Strategies (Springer-Verlag, NY).
4. Cerny, V. [1985] "Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm," J. Opt. Th. Appl. 45, 41-51.
5. Chen, G. & Dong, X. [1998] From Chaos to Order: Methodologies, Perspectives and Applications (World Scientific, Singapore).
6. Chen, G. & Ueta, T. [1999] "Yet another chaotic attractor," Int. J. Bifurcation and Chaos 9, 1465-1667.
7. Chen, G. [2000] Controlling Chaos and Bifurcations in Engineering Systems (CRC Press, Boca Raton).
8. Colin, G. J. [2003] "Artificial immune systems programming for symbolic regression," in Genetic Programming, eds. Ryan, C., Soule, T., Keijzer, M., Tsang, E., Poli, R. & Costa, E., Lecture Notes in Computer Science, Vol. 2610 (Springer-Verlag, Berlin), pp. 345-353.
9. Davis, L. [1996] Handbook of Genetic Algorithms (Van Nostrand Reinhold, Berlin).
10. Dmitriev, A. S., Panas, A. I. & Starkov, S. O. [1996] "Ring oscillating systems and their application to the synthesis of chaos generators," Int. J. Bifurcation and Chaos 6, 851-865.
11. Dmitriev, A. S., Efremova, E., Kuzmin, L. & Anagnostopoulos, A. [2001] "High dimensional RC -oscillators of chaos," 2001 Int. Symp. Nonlinear Theory and Its Applications, Miyagi, Japan, October 28 - November 1, 2001.
12. Dorigo, M. & Stützle, T. [2004] Ant Colony Optimization (MIT Press, MA).
13. Eberhart, R. C. & Kennedy, J. [1995] "A new optimizer using particle swarm theory," Proc. Sixth Int. Symp. Micromachine and Human Science, Nagoya, Japan, pp. 39-43.
14. Eguchi, K., Inoue, T. & Tsuneda, A. [1999] "Synthesis and analysis of a digital chaos circuit generating multiple-scroll strange attractors," IEICE Trans. Fundamentals E82-A, 965-972.
15. Garey, M. R. & Johnson, D. S. [1979] Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, NY).
16. Gilmore, R. & Lefranc, M. [2002] The Topology of Chaos: Alice in Stretch and Squeezeland (Wiley-Interscience, NY).
17. Grebogi, C. & Lai, Y. C. [1999] "Controlling chaos," in Handbook of Chaos Control, ed. Schuster, H. G. (Wiley-VCH, NY).
18. Hilborn, R. C. [1994] Chaos and Nonlinear Dynamics (Oxford University Press, UK).
19. Holland, J. H. [1975] Adaptation in Natural and Artificial Systems (Univ. Michigan Press, Ann Arbor).
20. Hu, G., Xie, F., Xiao, J., Yang, J. & Qu, Z. [1999] "Control of patterns and spatiotemporal chaos and its application," in Handbook of Chaos Control, ed. Schuster, H. G. (Wiley VCH, NY).
21. Just, W. [1999] "Principles of time delayed feedback control," in Handbook of Chaos Control, ed. Schuster, H. G. (Wiley-VCH, NY).
22. Just, W., Benner, H. & Reibold, E. [2003] "Theoretical and experimental aspects of chaos control by time-delayed feedback," Chaos 13, 259-266.
23. Kirkpatrick, S., Gelatt, C. D. & Vecchi, M. P. [1983] "Optimization by simulated annealing," Science 220, 671-680.
24. Koza, J. R. [1990] "Genetic Programming: A paradigm for genetically breeding populations of computer programs to solve problems," Stanford University, Computer Science Department, Technical Report STAN-CS-90-1314.
25. Koza, J. R. [1998] Genetic Programming (MIT Press, Boston).
26. Koza, J. R., Bennet, F. H., Andre, D. & Keane, M. [1999] Genetic Programming III (Morgan Kaufnamm, NY).
27. Koza, J. R., Keane, M. A. & Streeter, M. J. [2003] "Evolving inventions," Sci. Amer. 288, 40-47.
28. Lorenz, E. N. [1963] "Deterministic nonperiodic flow," J. Atmosph. Sci. 20, 130-141.
29. May, R. [1976] "Simple mathematical model with very complicated dynamics, Nature 261, 45-67.
30. Nolle, L., Zelinka, I., Hopgood, A. A. & Goodyear, A. [2005] "Comparison of an self organizing migration algorithm with simulated annealing and differential evolution for automated waveform tuning," Adv. Engin. Softw. 36, 645-653.
31. O'Neill, M. & Ryan, C. [2003] Grammatical Evolution, Evolutionary Automatic Programming in an Arbitrary Language (Springer-Verlag, NY).
32. O'Neill, M. & Brabazon, A. [2006] Grammatical differential evolution, in Proc. Int. Conf. Artificial Intelligence (ICAI'06) (CSEA Press), pp. 231-236.
33. Oplatkova, Z. [2005] "Optimal trajectory of robots using symbolic regression," Proc. 56th Int. Astronautics Congress 2005, Fukuoka, Japan, Paper Nr. IAC-05-C1.4.07.
34. Oplatkova, Z. & Zelinka, I. [2006] "Investigation on artificial ant using analytic programming," Proc. Genetic and Evolutionary Computation Conf. 2006, Seattle, WA, pp. 949-950.
35. Ott, E., Grebogi, C. & Yorke, J. A. [1990] "Controlling chaos," Phys. Rev. Lett. 64, 1196-1199.
36. Perruquetti, W. & Barbot, J. P. [2005] Chaos in Automatic Control (CRC, Bota Raton).
37. Price, K. [1994] "Genetic annealing," Dr. Dobb's J., October, 127-132.
38. Price, K. [1996] "Differential evolution: A fast and simple numerical optimizer," Proc. 1996 Biennial Conf. North American Fuzzy Information Processing Society (IEEE Press, NY), pp. 524-527.
39. Price, K. [1999] An Introduction to Differential Evolution, New Ideas in Optimization, eds. Corne, D., Dorigo, M. & Glover, F. (McGraw-Hill, London, UK), pp. 79-108.
40. Pyragas, K. [1992] "Continuous control of chaos by self-controlling feedback," Phys. Lett. A 170, 421-428.
41. Richter, H. & Reinschke, K. J. [2000] "Optimization of local control of chaos by an evolutionary algorithm," Physica D 144, 309-334.
42. Richter, H. [2002] "An evolutionary algorithm for controlling chaos: The use of multi-objective fitness functions," in Parallel Problem Solving from Nature-PPSN VII, eds. Merelo Guervós, J. J., Panagiotis, A., Beyer, H. G., Fernández Villacanas, J. L. & Schwefel, H. P., Lecture Notes in Computer Science, Vol. 2439 (Springer-Verlag, Berlin), pp. 308-317.
43. Ryan, C., Collins, J. J. & O'Neill, M. [1998] Grammatical Evolution: Evolving Programs for an Arbitrary Language, Lecture Notes in Computer Science, Vol. 1391, First European Workshop on Genetic Programming.
44. Schuster, H. G. [1999] Handbook of Chaos Control (Wiley-VCH, NY).
45. Stewart, I. [2000] "The Lorenz attractor exists," Nature 406, 948-949.
46. Ueta, T. & Chen, G. [2000] "Bifurcation analysis of Chen's attractor," Int. J. Bifurcation and Chaos 10, 1917-1931.
47. Vanecek, A. & Celikovsky, S. [1994] "Chaos synthesis via root locus," IEEE Trans. Circuits Syst. 41, 59-60.
48. Vanecek, A. & Celikovsky, S. [1996] Control Systems: From Linear Analysis to Synthesis of Chaos (Prentice-Hall, London).
49. Wang, X. & Chen, G. [2000] "Chaotification via arbitrarily small feedback controls: Theory, method, and applications," Int. J. Bifurcation and Chaos 10, 549-570.
50. Zelinka, I. [2001] "Analytic programming by means of new evolutionary algorithms," Proc. 1st Int. Conf. New Trends in Physics'01, Brno, Czech Republic, pp. 210-214.
51. Zelinka, I. [2002] "Analytic programming by means of soma algorithm," ICICIS'02, First Int. Conf. Intelligent Computing and Information Systems (Cairo, Egypt), pp. 148-154.
52. Zelinka, I. & Oplatkova, Z. [2003] "Analytic programming - comparative study," Proc. Second Int. Conf. Computational Intelligence, Robotics, and Autonomous Systems, Singapore, Paper No. PS04-2-04.
53. Zelinka, I. [2004] "SOMA - Self organizing migrating algorithm," in New Optimization Techniques in Engineering, eds. Babu, B. V. & Onwubolu, G. (Springer-Verlag, NY), pp. 167-218.
54. Zelinka, I. & Nolle, L. [2005] "Plasma reactor optimizing using differential evolution," in Differential Evolution: A Practical Approach to Global Optimization, eds. Price, K. V., Lampinen, J. & Storn, R. (Springer-Verlag, NY), pp. 499-512.
55. Zelinka, I., Oplatkova, Z. & Nolle, L. [2005] "Analytic programming - symbolic regression by means of arbitrary evolutionary algorithms," Int. J. Simul. Syst. Sci. Technol. 6, 44-56.
56. Zelinka, I. & Volna, E. [2005] "Neural network synthesis by means of analytic programming - preliminary results," Proc. 11th Int. Conf. Soft Computing Mendel'05, Brno, Czech Republic.
57. Zelinka, I. [2005] "Investigation on evolutionary deterministic chaos control," Proc. IFAC, Prague, Czech Republic, Paper No. 03187.
58. Zelinka, I. [2006] "Investigation on realtime deterministic chaos control by means of evolutionary algorithms," Proc. First IFAC Conf. Analysis and Control of Chaotic Systems (Reims, France), pp. 211-217.
59. Zhou, T., Chen, G. & Ĉelikovský, S. [2005] "An algorithm for computing heteroclinic orbits and its application to chaos synthesis in the generalized Lorenz system," Proc. 16th World Congress of the International Federation of Automatic Control [CD-ROM ], Praha, Czech Republic.
60. Zou, Y.-L., Luo, X.-S. & Chen, G. [2006] "Pole placement method of controlling chaos in DC - DC buck converters," Chinese Phys. 15, 1719-1724.