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Control techniques for chaotic dynamical systems. (English) Zbl 0809.34058
This article is a short summary of recent research activity regarding stabilization and control of chaotic dynamical systems. The extensive list of references dealing with various specific methods and examples should serve a useful purpose.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93C10 Nonlinear systems in control theory
93D15 Stabilization of systems by feedback
34H05 Control problems involving ordinary differential equations
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References:
[1] E. H. Abed H. O. Wang, R. C. Chen: Stabilization of period doubling bifurcations and implications for control of chaos. Proc. 31st IEEE Conference on Decision and Control, Tucson 1992, pp. 2119-2124.
[2] F. Albertini, E. D. Sontag: Some connections between chaotic dynamical systems and control systems. Proc. 1st European Control Conference, Grenoble 1991, pp. 158-163.
[3] D. P. Atherton: Nonlinear Control Engineering. Van Nostrand Reinhold, London 1975.
[4] Y. Braiman, I. Goldhirsch: Taming chaotic dynamics with weak periodic perturbations. Phys. Rev. Lett. 66 (1991), 2545-2548. · Zbl 0968.37508
[5] T. L. Carrol, L.M. Pecora: A circuit for studying the synchronization of a chaotic system. Internat. J. Bifur. Chaos Appl. Sci. Engng. 2 (1992), 659-667. · Zbl 0873.58045
[6] G. Chen, X. Dong: On feedback control of chaotic nonlinear dynamic systems. Internat. J. Bifur. Chaos Appl. Sci. Engng. 2 (1992), 407-412. · Zbl 0875.93176
[7] G. Chen, X. Dong: From chaos to order- Prespectives and methodologies in controlling chaotic nonlinear dynamical systems. Systems Control and Computing, Tech. Rep. 92-07, University of Houston, Houston 1992.
[8] L. O. Chua: The genesis of Chua’s circuit. Archiv fur Elektronik und Ubertragungstechnik 47 (1992), 250-257.
[9] F. Colonius, W. Klienman: On control sets and feedback for nonlinear systems. Preprints 2nd 1FAC Symposium NOLCOS, Bordeaux 1992, pp. 29-36.
[10] A. Dabrowski Z. Galias, M.J. Ogorzalek: A study of identification and control in a real implementation of Chua’s circuit. Preprints 2nd IFAC Workshop on System Structure and Control, Prague 1992, pp. 278-281.
[11] W. L. Ditto S. N. Rauseo, M. L. Spano: Experimental control of Chaos. Phys. Rev. Lett. 25 (1990), 3211-3214.
[12] U. Dressier, G. Nitsche: Controlling Chaos using time delay coordinates. Phys. Rev. Lett. 68 (1992), 1-4.
[13] W. H. Fleming (ed.): Report of the panel on future directions in control theory: a mathematical perspective. Society for Industrial and Applied Mathematics, Philadelfia 1988.
[14] T. B. Fowler: Application of stochastic control techniques to chaotic nonlinear systems. IEEE Trans. Automat. Control AC-34 (1989), 201-205. · Zbl 0677.93072
[15] R. Genesio, A. Tesi: Chaos prediction in nonlinear feedback systems. IEE Proc. D Control Theory and Applications 138 (1991), 313-320. · Zbl 0754.93024
[16] R. Genesio, A. Tesi: Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems. Automatica 28 (1992), 531-548. · Zbl 0765.93030
[17] R. Genesio, A. Tesi: A harmonic balance approach for chaos prediction: the Chua’s circuit. Internat. J. Bifur. Chaos Appl. Sci. Engng. 2 (1992), 61-79. · Zbl 0874.94042
[18] R. Genesio, A. Tesi: Distortion Control of chaotic systems: the Chua’s circuit. J. Circuits, Systems and Computers 5 (1993), 151-171.
[19] A. Hiibler: Adaptive control of chaotic systems. Helv. Phys. Acta 62 (1989), 343-346.
[20] A. Hiibler: Modeling and control of complex systems: paradigms and applications. Modeling Complex Phenomena (L. Lam and V. Naroditsky, Springer-Verlag, New York 1992, pp. 5-65.
[21] E. R. Hunt: Stabilizing high-period orbits in a chaotic system: the diode resonator. Phys. Rev. Lett. 57 (1992), 1953-1955.
[22] H. Hyotyniemi: Postponing Chaos using a robust stabilizer. Proc. 1st IFAC Symposium on Design Methods of Control Systems, Zurich 1991, pp. 568-572.
[23] E. A. Jackson: The entrainment and migration controls of multiple-attractor systems. Phys. Lett. A 151 (1990), 478-484.
[24] E. A. Jackson: O: n the control of complex dynamic systems. Phys. Lett. D 50 (1991), 341-366. · Zbl 0746.93041
[25] J. H. Kim, J. Stringer (eds.): Applied Chaos. John Wiley, New York 1992. · Zbl 0876.00014
[26] H. C. Lee., E. H. Abed: Washout filters in the bifurcation control of high alpha flight dynamics. Proc. 1991 IEEE Amer. Contr. Conf., Boston 1991.
[27] R. Lima, M. Pettini: Suppression of Chaos by resonant parametric perturbations. Phys. Rev. 41 (1991), 1726-1733.
[28] R. Madan (ed.): Special Issue on Chua’s circuit: A paradigm for chaos. Part I. J. Circuits, Systems and Computers 3 (1993), 1. · Zbl 0861.58026
[29] R. Madan (ed.): Special Issue on Chua’s circuit: A paradigm for chaos. Part II. J. Circuits, Systems and Computers 5 (1993), 2. · Zbl 0861.58026
[30] A.I. Mees: Dynamics of Feedback Systems. John Wiley, New York 1981. · Zbl 0454.93003
[31] M. Mohler: Nonlinear systems: Dynamics and Control. Vol. I. Prentice Hall, Englewood Cliffs 1991. · Zbl 0752.93032
[32] F. Mossayebi H. K. Qammar, T. T. Hartley: Adaptive estimation and synchronization of chaotic systems. Phys. Lett. A 161 (1991), 255-262.
[33] E.C. Ott C. Grebogi, J. A. Yorke: Controlling Chaos. Phys. Rev. Lett. 64 (1990), 1196-1199. · Zbl 0964.37501
[34] B. Peng V. Petrov, and K. Showalter: Controlling Chemical Chaos. J. Phys. Chem. 95 (1991), 4957-4959.
[35] R. Rajasekar, M. Lakshmanan: Controlling of chaos in Bonhoeffer-van der Poloscillator. Internat. J. Bifur. Chaos Appl. Sci. Engng. 2 (1992), 201-204. · Zbl 0875.93192
[36] F. J. Romeiras E. Ott C. Grebogi, W. P. Dayawansa: Controlling chaotic dynamical systems. Proc. 1991 IEEE Amer. Control Conference, Boston 1991. · Zbl 1194.37140
[37] R. Roy T.W. Murphy, Jr. T.D. Maier Z. Gills, and E. R. Hunt: Dynamical control of a chaotic laser: experimental stabilization of a globally coupled system. Phys. Rev. Lett. 68 (1992), 1259-1262.
[38] T. Shinbrot E. Ott C. Grebogi, J. A. Yorke: Using Chaos to direct trajectories to targets. Phys. Rev. Lett. 65 (1990), 3215-3218.
[39] D. D. Siljak: Nonlinear Systems: the Parameter Analysis and Design. John Wiley, New York 1969. · Zbl 0194.39302
[40] J. Singer Y. Z. Wang, H. H. Bau: Controlling a chaotic system. Phys. Rev. Lett. 66 (1991), 1123-1125.
[41] S. Sinha R. Ramaswamy, J. S. Rao: A: daptive control in nonlinear dynamics. Phys. Lett. D 43 (1990), 118-128. · Zbl 0703.93041
[42] T. Taylor: Chaos and its applications in control. Proc. 31st IEEE Conference on Decision and Control, Tucson 1992, pp. 2102-2106.
[43] A. Vaněček: Strongly nonlinear and other control systems. Problems Control Inform. Theory 20 (1991), 3-12. · Zbl 0747.93033
[44] M. Vidyasagar: Nonlinear System Analysis. Prentice-Hall, Englewood Cliffs 1978.
[45] T. L. Vincent, J. Yu: Control of a chaotic system. Dynamics and Control 1 (1991), 35-52. · Zbl 0747.93071
[46] H. O. Wang, E. H. Abed: Bifurcation control of chaotic dynamical systems. Preprints 2nd IFAC Symposium NOLCOS, Bordeaux, France, 1992.
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