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Control of Chaos: Methods and Applications. II. Applications

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Abstract

Reviewed were the problems and methods for control of chaos, which in the last decade was the subject of intensive studies. Consideration was given to their application in various scientific fields such as mechanics (control of pendulums, beams, plates, friction), physics (control of turbulence, lasers, chaos in plasma, and propagation of the dipole domains), chemistry, biology, ecology, economics, and medicine, as well as in various branches of engineering such as mechanical systems (control of vibroformers, microcantilevers, cranes, and vessels), spacecraft, electrical and electronic systems, communication systems, information systems, and chemical and processing industries (stirring of fluid flows and processing of free-flowing materials)).

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REFERENCES

  1. Alekseev, V.V. and Loskutov, A.Yu., Parametric Action-based Destochatization of the System with Strage Attractor, Vestn. Mosk. Gos. Univ., Mat. Mekh. Fiz. Astron., 1985, vol. 26, no. 3, pp. 40–44.

    Google Scholar 

  2. Alekseev, V.V. and Loskutov, A.Yu., On the Possibility of Controlling a System with Strage Attractor, in Problemy ekologicheskogo monitoringa i modelirovaniya ekosistem (Problems of Ecological Monitoring and Modeling of Ecosystems), Leningrad: Gidrometeoizdat, 1985, vol. VIII.

    Google Scholar 

  3. Andreev, Yu.V., Dmitriev, A.S., and Kuminov, D.A., Chaotic Processors, Usp. Sovrem. Radioelektr. (Zarub. Radioelektron.), 1997, no. 10, pp. 50–79.

  4. Andrievskii, B.R. and Fradkov, A.L., Control of Nonlinear Oscillatory and Chaotic Systems, Ch. 13, in Izbrannye glavy teorii avtomaticheskogo upravleniya (Selected Chapters of the Automatic Control Theory), St. Petersburg: Nauka, 1999.

    Google Scholar 

  5. Andrievskii, B.R. and Fradkov, A.L., Elementy matematicheskogo modelirovania v programmnyh sredakh MATLAB 5 i Scilab (Elements of Mathematical Modeling in MATLAB 5 and Scilab Program Environments), St. Petersburg: Nauka, 2001.

    Google Scholar 

  6. Andrievskii, B.R. and Fradkov, A.L., Control of Chaos: Methods and Applications. I. Methods, Avtom. Telemekh., 2003, no. 5, pp. 3–45.

  7. Volkovskii, A.R. and Rul'kov, N.F., Lett. Zh. Teor. Fiz., 1993, no. 19, p. 3.

  8. Ginzburg, N.S., Zaitsev, N.I., Il'akov, E.V., et al., Chaotic Generation in the Megawatt Backward-wave Tubes, Zh. Teor. Fiz., 2001, vol. 71, no. 11, pp. 73–80.

    Google Scholar 

  9. Glumov, V.M., Zemljakov, S.D., Rutkovskii, V.Yu., and Suhanov, V.M., Spatial Angular Motion of the Flexible Spacecraft: The Modal-physical Model and Its Characteristics, Avtom. Telemekh., 1998, no. 12, pp. 38–50.

  10. Dmitriev, A.S., Panas, A.I., and Starkov, S.O., Dynamic Chaos as a Paradigm of the Modern Communication Systems, Zarub. Radioelektron., 1997, no. 10, pp. 4–26.

  11. Dmitriev, A.S. and Kuz'min, L.V., Information Transmission Using Synchronous Chaotic Response in the Presence of Filtering in Communication Channel, Lett. Zh. Teor. Fiz., 1999, vol. 25, no. 16, pp. 71–77.

    Google Scholar 

  12. Dmitriev, A.S. and Panas, A.I., Dinamicheskii khaos: novye nositeli informatsii dlya sistem svyazi (Dynamic Chaos: New Data Carriers for Communication Systems), Moscow: Nauka, 2002.

    Google Scholar 

  13. Dmitriev, A.A., Chaotic Sequences Containing Given Information, Radiotekh. Elektron., 2002, vol. 47, no. 11, pp. 1370–1375.

    Google Scholar 

  14. Loiko, N.A., Naumenko, A.V., and Turovets, S.I., Action of the Pyragas Feedback on Dynamics of the Laser with Modulatin of Losses, Zh. Eksp. Teor. Fiz., 1997, vol. 112, no. 4 (10), pp. 1516–1530.

    Google Scholar 

  15. Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (Nonlinear and Adaptive Control of Complex Dynamic Systems), St. Petersburg: Nauka, 2000.

    Google Scholar 

  16. Moon, F., Chaotic and Fractal Dynamics: An Introduction for Applied Scientists and Engineers, New York: Wiley, 1992. Translated under the title Khaoticheskie kolebaniya, Moscow: Mir, 1990.

    Google Scholar 

  17. Napartovich, A.P. and Suharev, A.G., Information Decoding in the Chaotic Laser System Controlled by Chaotic Signal, Kvantovaya Elektron., 1998, vol. 25, no. 1, pp. 85–88.

    Google Scholar 

  18. Nejmark, Yu.I. and Landa, P.S. Stokhasticheskie i khaoticheskie kolebaniya (Stochastic and Chaotic Oscillations), Moscow: Nauka, 1987.

    Google Scholar 

  19. Rabinovich, M.I. and Trubetskov, D.I., Vvedenie v teoriyu kolebanii i voln (Introduction to the Theory of Oscillations and Waves), Moscow: Nauka, 1984.

    Google Scholar 

  20. Fradkov, A.L., Feedback-based Study of Physical Systems, Avtom. Telemekh., 1999, no. 3, pp. 213–230.

  21. Fradkov, A.L. and Andrievskii, B.R., Damping of Spacecraft Oscillations by Small-poer Control, Tez. X SPb. mezhd. konf. po integrirovannym navigatsionnym sistemam (Proc. X St. Petersburg Int. Conf. on Integrated Navigation Systems), St. Petersburg: GNC RF-CNII “Elektropribor”, 2003.

    Google Scholar 

  22. Fradkov, A.L., Kiberneticheskaya fizika: principy i primery (Cybernetical Physics: Principles and Examples), St. Petersburg: Nauka, 2003.

    Google Scholar 

  23. Khramov, A.E. and Rempen, I.S., Impact of Delayed-time Feedback on Complex Dynamics in the Hydrodynamic Pierce Model, Radiotekh. Elektron., 2002, vol. 47, no. 6, pp. 732–738.

    Google Scholar 

  24. Shalfeev, V.D., Osipov, G.V., Kozlov, A.K., and Volkovskii, A.R., Chaotic Oscillations: Generation, Synchronization, Control, Zarub. Radioelektron. Usp. Sovr. Radioelektron., 1997, no. 10, pp. 27–49.

  25. Shimanskii, V.E., Communication System with Chaotic Carrier Based on the ADSP-2181 Digital Signal Processor, Izv. Vuzov, Prikl. Nelin. Dinam., 1998, vol. 6, no. 5, pp. 66–75.

    Google Scholar 

  26. Abel, A. and Schwarz, W., Chaos Communication Principles, Schemes, and System Analysis, Proc. IEEE, 2002, vol. 90, no. 5, pp. 691–710.

    Google Scholar 

  27. Aliev, K.M., Kamilov, I.K., Ibragimov, Kh.O., and Abakarova, N.S., Synchronization of Chaos and Small Signal Amplification in Electron-Hole Plasma of Germanium, in Proc. 2003 Int. Conf.Physics and Control” Fradkov, A.L. and Churilov, A.N., Eds., St. Petersburg, Russia, 2003, pp. 675–679.

  28. Alvarez-Ramirez, J., Puebla, H., and Cervantes, I., Stability of Observer-Based Chaotic Communications for a Class of Lur'e Systems, Int. J. Bifurcat. Chaos, 2002, vol. 12, no. 7, pp. 1605–1618.

    Google Scholar 

  29. Amann, A., Schöll, E., Baba, N., and Just, W., Time Delayed Feedback Control of Chaos by Spatio-Temporal Filtering, 2003 Int. Conf. “Physics and Control,” St. Petersburg, 2003 (http://www.rusycon.ru).

  30. Anderson, P.D., Galaktionov, O.S., Peters, G.W.M., van de Vosse, F.N., and Meijer, H.E.H., Chaotic Fluid Mixing in Non-Quasi-Static Time-Periodic Cavity Flows, Int. J. Heat Fluid Flow, 2000, vol. 21, pp. 176–

    Google Scholar 

  31. Andrievsky, B. and Fradkov, A., Information Transmission by Adaptive Synchronization with Chaotic Carrier and Noisy Channel, Proc. 39th IEEE Conf. Dec. Contr., Sydney, 2000.

  32. Andrievsky, B.R., Adaptive Synchronization Methods for Signal Transmission on Chaotic Carriers, Math. Comput. Simulation, 2002, vol. 58, no. 4-6, pp. 285–293.

    Google Scholar 

  33. Andrievsky, B.R., Boykov, K.B., and Fradkov, A.L., Numerical and Experimental Excitability Analysis of Multi-Pendulum Mechatronics System, 15th IFAC World Congress on Automatic Control, Barcelona, July 2002.

  34. Anishchenko, V.S. and Pavlov, A.N., Global Reconstruction in Application to Multichannel Communication, Phys. Revol. E, 1998, vol. 57, no. 2, pp. 2455–2457.

    Google Scholar 

  35. Ashhab, M., Salapaka, M.V., Dahleh, M., and Mezic, I., Control of Chaos in Atomic Force Microscopes, Am. Contr. Conf., 1997, vol. 1, pp. 196–202.

    Google Scholar 

  36. Ashhab, M., Salapaka, M.V., Dahleh, M., and Mezic, I., Dynamical Analysis and Control of Microcantilevers, Automatica, 1999, vol. 35, pp. 1663–1670.

    Google Scholar 

  37. Bai, E.-W., Lonngren, K.E., and Sprott, J.C., On the Synchronization of a Class of Electronic Circuits That Exhibit Chaos, Chaos, Solitons, Fractals, 2002, vol. 13, pp. 1515–1521.

    Google Scholar 

  38. Baptista, M.S., Cryptography with Chaos, Phys. Lett. A, 1998, vol. 240, pp. 50–54.

    Google Scholar 

  39. Baptista, M.S., Macau, E.E., Grebogi, C., et al., Integrated Chaotic Communication Scheme, Phys. Revol. E, 2000, vol. 64, no. 4, pp. 4835–4845.

    Google Scholar 

  40. Baptista, M.S., Macau, E.E., and Grebogi, C., Conditions for Efficient Chaos-Based Communication, Chaos, 2003, vol. 13, no. 1, pp. 145–150.

    Google Scholar 

  41. Barratt, C., On the Control of Chaos in Extended Structures, J. Vibration AcousticsTrans. ASME, 1997, vol. 119, pp. 551–556.

    Google Scholar 

  42. Batlle, C., Fossas, E., and Olivar, G., Stabilization of Periodic Orbits of the Buck Converter by Time-Delayed Feedback, Int. J. Circ. Theory Appl., 1999, vol. 27, pp. 617–631.

    Google Scholar 

  43. Bishop, S.R. and Xu, D., The Use of Control to Eliminate Subharmonic and Chaotic Impacting Motions of a Driven Beam, J. Sound Vibr., 1997, vol. 205, pp. 223–234.

    Google Scholar 

  44. Brandt, M.E., Shih, H.T., and Chen, G.R., Linear Time-delay Feedback Control of a Pathological Rhythm in a Cardiac Conduction Model, Phys. Revol. E, 1997, vol. 56, pp. 1334–1337.

    Google Scholar 

  45. Brone, D. and Muzzio, F.J., Size Segregation in Vibrated Granular Systems: A Reversible Process, Phys. Revol. E, 1997, vol. 56, no. 1, pp. 1059–1063.

    Google Scholar 

  46. Chaos in Chemistry and Biochemistry, Field, R.J. and Gyorgyi, L., Eds., Singapore: World Scientific, 1992.

    Google Scholar 

  47. Chaos and Non-linear Models in Economics. Theory and Applications, Creedy, J. and Martin, V.L., Eds., Melbourne: Edward Elgar, 1994.

    Google Scholar 

  48. Chen, J.H., Chau, K.T., Siu, S.M., and Chan, C.C., Experimental Stabilization of Chaos in a Voltage-Mode Dc Drive System, IEEE Trans. Circ. Syst. I, 2000, no. 47, pp. 1093–1095.

  49. Chen, L.Q. and Cheng, C.J., Controlling Chaotic Oscillations of Viscoelastic Plates by the Linearization via Output Feedback, App. Math. Mech. Engl. Ed., 1999, no. 220, pp. 1324–1330.

  50. Chen, H.-K., Chaos and Chaos Synchronization of a Symmetric Gyro with Linear-Plus-Cubic Damping, J. Sound Vibr., 2002, vol. 255, no. 4, pp. 719–740.

    Google Scholar 

  51. Chen, Li-Qun and Liu Yan-Zhu, Chaotic Attitude Motion of a Magnetic Rigid Spacecraft and Its Control, Int. J. Non-Linear Mechanics, 2002, vol. 37, pp. 493–504.

    Google Scholar 

  52. Gluckman, B.J., Control of Seizing Neuronal Networks, in Experimental Chaos. 6th Experimental Chaos Conf., Potsdam, Germany, 2001, AIP Conf. Proc., Boccaletti, S., Gluckman, B.J., Kurths, J., et al., New York, 2002, vol. 622, pp. 105–107.

  53. Cuomo, K.M., Oppenheim, A.V., and Strogatz, S.H., Synchronization of Lorenz-based Chaotic Circuits with Application to Communications, IEEE Trans. Circ. Syst.II, 1993, vol. 40, no. 10, pp. 626–633.

    Google Scholar 

  54. Cuomo, K.M. and Oppenheim, A.V., Circuit Implementation of Synchronized Chaos with Applications to Communications, Phys. Rew. Lett., 1993, vol. 71, no. 1, pp. 65–68.

    Google Scholar 

  55. Complexity, Chaos, and Biological Evolution, NATO ASI Series, ser. B: Physics, Mosekilde, E. and Mosekilde, L., Eds., New York: Plenum, 1991, vol. 270.

    Google Scholar 

  56. D'Alessandro, D., Dahleh, M., and Mezic, I., Control of Mixing in Fluid Flow: A Maximum Entropy Approach, IEEE Trans. Automat. Control, 1999, vol. 44, no. 10, pp. 1852–1863.

    Google Scholar 

  57. Davies, M.L., Halford-Maw, P.A., Hill, J., Tinsley, M.R., Johnson, B.R., Scott, S.K., Kiss, I.Z., and Gáspár, V., Control of Chaos in Combustion Reactions, J. Phys. Chem. A, 2000, vol. 104, pp. 9944–9952.

    Google Scholar 

  58. Dedieu, H. and Ogorzalek, M., Chaos Based Information Processing, Int. J. Bifurcat. Chaos, 2000, vol. 10, no. 4, pp. 737–748.

    Google Scholar 

  59. Desharnais, R.A., Costantino, R.F., Cushing, J.M., et al., Chaos and Population Control of Insect Outbreaks, Ecology Lett., 2001, vol. 4, 229–235.

  60. Dhamala, M. and Lai, Y.C., Controlling Transient Chaos in Deterministic Flows with Applications to Electrical Power Systems and Ecology, Phys. Revol. E, 1999, vol. 59, pp. 1646–1655.

    Google Scholar 

  61. Ditto, W.L., Spano, M.L., In, V., Neff, J., Meadows, B., Langberg, J.J., Bolmann, A., and McTeague, K., Control of Human Atrial Fibrillation, Int. J. Bifurcat. Chaos, 2000, vol. 10, pp. 593–601.

    Google Scholar 

  62. Dmitriev, A., Andreev, Yu., Belsky, Yu., et al., US Patent 5774587: Method of Objects Recognition, Dec. 1, 1995.

  63. Dolov, A.M. and Kuznetsov, S.P., Application of Idea of Chaos Control to Stabilization of Stationary Generation in Backward-Wave Oscillator, in Proc. 2003 Int. Conf.Physics and Control”, Fradkov, A.L. and Churilov, A.N., Eds., St. Petersburg, Russia, 2003, pp. 507–509.

  64. Dykstra, R., Tang, D.Y., and Heckenberg, N.R., Experimental Control of Single-Mode Laser Chaos by Using Continuous, Time-Delayed Feedback, Phys. Revol. E, 1998, vol. 57, pp. 6596–6598.

    Google Scholar 

  65. Elmer, F.J., Controlling Friction, Phys. Revol. E, 1998, vol. 57, pp. 4903–4906.

    Google Scholar 

  66. Fang, C.C. and Abed, E.H., Robust Feedback Stabilization of Limit Cycles in Pwm Dc-Dc Converters, Nonlin. Dynam., 2002, vol. 27, pp. 295–309.

    Google Scholar 

  67. Feki, M., An Adaptive Chaos Synchronization Scheme Applied to Secure Communication, Chaos, Solitons, Fractals, 2003, vol. 18, pp. 141–148.

    Google Scholar 

  68. Femat, R., Jauregui-Ortiz, R., and Solís-Perales, G., A Chaos-Based Communication Scheme via Robust Asymptotic Feedback, IEEE Trans. Circ. Syst. I, 2001, vol. 48, pp. 1161–1169.

    Google Scholar 

  69. Feudel, U. and Grebogi, C., Multistability and the Control of Complexity, Chaos, 1997, vol. 7, pp. 597–604.

    Google Scholar 

  70. Fradkov, A.L. and Pogromsky, A.Yu., Introduction to Control of Oscillations and Chaos, Singapore: World Scientific, 1998.

    Google Scholar 

  71. Fradkov, A.L., Nijmeijer, H., and Markov, A.Yu., Adaptive Observer-based Synchronization for Communication, Int. J. Bifurcat. Chaos, 2000, vol. 10, no. 12, pp. 2807–2813.

    Google Scholar 

  72. Fradkov, A.L. and Andrievsky, B.R., Adaptive Robustied Synchronization Methods for Chaos-based Information Transmission, Proc. 1st IEEE Int. Conf. Circ. Syst. for Communic., St. Petersburg, 2002, pp. 275–280.

  73. Fradkov, A.L., Nikiforov, V.O., and Andrievsky, B.R., Adaptive Observers for Nonlinear Nonpassifiable Systems with Application to Signal Transmission, Proc. 41st IEEE Conf. Dec. and Contr. (CDC '02), USA, 2002, pp. 47046–4711.

  74. Friedel, H., Grauer, R., and Spatschek, K.H., Controlling Chaotic States of a Pierce Diode, Phys. Plasmas, 1998, vol. 5, pp. 3187–3194.

    Google Scholar 

  75. Gad-el-Hak, M., Flow Control: Passive, Active, and Reactive Flow Management, London: Cambridge Univ. Press, 2000.

    Google Scholar 

  76. Garfinkel, A., Spano, M.L., Ditto, W.L., and Weiss, J.N., Controlling Cardiac Chaos, Science, 1992, vol. 257, pp. 1230–1235.

    Google Scholar 

  77. Ge, Z.-M. and Lin, T.-N., Chaos, Chaos Control and Synchronization of Electro-Mechanical Gyrostat System, J. Sound Vibr., 2003, vol. 259, no. 3, pp. 585–603.

    Google Scholar 

  78. Ge, Z.M. and Shiue, J.S., Non-linear Dynamics and Control of Chaos for a Tachometer, J. Sound Vibr., 2002, vol. 253.

  79. Ghezzi, L.L. and Piccardi, C., PID Control of a Chaotic System: An Application to an Epidemiological Model, Automatica, 1997, vol. 33, pp. 181–191.

    Google Scholar 

  80. Giona, M., Functional Reconstruction of Oscillating Reaction: Prediction and Control of Chaotic Kinetics, Chem. Engr. Sci., 1992, vol. 47, pp. 2469–2474.

    Google Scholar 

  81. Glorieux, P., Control of Chaos in Lasers by Feedback and Nonfeedback Methods, Int. J. Bifurcat. Chaos, 1998, vol. 8, pp. 1749–1758.

    Google Scholar 

  82. Guderian, A., Munster, A.F., Jinguji, M., Kraus, M., and Schneider, F.W., Resonant Chaos Control by Light in a Chemiluminescent Reaction, Chem. Phys. Lett., 1999, vol. 312, pp. 440–446.

    Google Scholar 

  83. Habel, R. and Beige, H., Ferroelectric Systems with Controlled Chaos, Int. J. Bifurcat. Chaos, 1997, vol. 7, pp. 199–204.

    Google Scholar 

  84. Harb, A.M. and Abdel-Jabbar, N., Controlling Hopf Bifurcation and Chaos in a Small Power System, Chaos, Solitons, Fractals, 2003, vol. 18, pp. 1055–1063.

    Google Scholar 

  85. He, S., Stabilizing the Richardson Eigenvector Algorithm by Controlling Chaos, Comput. Phys., 1997, vol. 11, pp. 194–198.

    Google Scholar 

  86. Heertjes, M.F. and Van de Molengraft, M.J.G., Controlling the Nonlinear Dynamics of a Beam System, Chaos, Solitons, Fractals., 2001, vol. 12, pp. 49–66.

    Google Scholar 

  87. Hill, K.M., Gilchrist, J.F., Ottino, J.M., Khakhar, D.V., and McCarthy, J.J., Mixing of Granular Materials: A Test-Bed Dynamical System for Pattern Formation, Int. J. Bifurcat. Chaos, 1999, vol. 9, pp. 1467–1484.

    Google Scholar 

  88. Holt, T.A., A Chaotic Model for Tight Diabetes Control, Diabetic Medicine, 2002, vol. 19, pp. 274–278.

    Google Scholar 

  89. Hołyst, J.A., Hagel, T., and Haag, G., Destructive Role of Competition and Noise for Control of Microeconomical Chaos, Chaos, Solitons, Fractals, 1997, vol. 8, pp. 1489–1505.

    Google Scholar 

  90. Hołyst, J.A. and Urbanowicz, K., Chaos Control in Economical Model by Time-Delayed Feedback Method, Physica A, 2000, vol. 287, pp. 587–598.

    Google Scholar 

  91. Hołyst, J.A., Źebrowska, M., and Urbanowicz, K., Observations of Deterministic Chaos in Financial Time Series by Recurrence Plots, Can One Control Chaotic Economy?, Eur. Phys. J. B, 2001, vol. 20, pp. 531–535.

    Google Scholar 

  92. Ibragimov, Kh.O., Aliev, K.M., Kamilov, I.K., and Abakarova, N.S., Chaos in Germanium Oscillistor, in Proc. 2003 Int. Conf.“ Physics and Control”, Fradkov, A.L. and Churilov, A.N., Eds., St. Petersburg, Russia, 2003, pp. 680–682.

  93. IEEE Transactions on Circuits and Systems. Special Issue “Chaos Control and Synchronization”, Kennedy, M. and Ogorzalek, M., Eds., 1997, vol. 44, no. 10.

  94. IEEE Transactions on Circuits and Systems. Special Issue on Applications of Chaos in Modern Communication Systems, Kocarev, L., Maggio, G.M., Ogorzalek, M., et al., Eds., 2001, vol. 48, no. 12.

  95. Iñarrea, M. and Lanchares, V., Chaos in the Reorientation Process of a Dual-Spin Spacecraft with Time-Dependent Moments of Inertia, Int. J. Bifurcat. Chaos, 2000, vol. 10, no. 5, pp. 997–1018.

    Google Scholar 

  96. Int. J. Circuit Theory and Applications, Special Issue: Communications, Information Processing and Control Using Chaos, Hasler, M. and Vandewalle, J., Eds., 1999, vol. 27, no. 6.

  97. Ishii, S. and Sato, M., Associative Memory Based on Parametrically Coupled Chaotic Elements, Physica D, 1998, vol. 121, pp. 344–366.

    Google Scholar 

  98. Kaart, S., Schouten, J.C., and van den Bleek, C.M., Synchronizing Chaos in an Experimental Chaotic Pendulum Using Methods from Linear Control Theory, Phys. Revol. E, 1999, vol. 59, pp. 5303–5312.

    Google Scholar 

  99. Kaart, S., Schouten, J.C., and van den Bleek, C.M., Improving Conversion and Selectivity of Catalytic Reactions in Bubbling Gas-Solid Fluidized Bed Reactors by Control of the Nonlinear Bubble Dynamics, Catalysis Today, 1999, vol. 48, pp. 185–194.

    Google Scholar 

  100. Kaplan, B.Z., Horen, Y., Cohen, G., and Hellerman, Y., Magnetic Levitation by Chaotic Oscillation: A New Method, IEEE Trans. Magnetics, 2002, vol. 38, no. 5, pp. 3475–3481.

    Google Scholar 

  101. Kennedy, M.P. and Kolumban, G., Digital Communications Using Chaos, in Controlling Chaos and Bifurcations in Engineering Systems, Chen, G., Ed., Boca Raton: CRC Press, 1999, pp. 477–500.

    Google Scholar 

  102. Khakhar, D.V., McCarthy, J.J., Shinbrot, T., and Ottino, J.M., Transverce Flow and Mixing of Granular Materials in a Rotating Cylinder, Phys. Fluids, 1997, vol. 9, pp. 31–43.

    Google Scholar 

  103. Khakhar, D.V., McCarthy, J.J., Gilchrist, J.F., and Ottino, J.M., Chaotic Mixing of GranularMaterials in Two-Dimensional Tumbling Mixers, Chaos, 1999, vol. 9, pp. 195–205.

    Google Scholar 

  104. Kimiaghalam, B., Homaifar, A., and Bikdash, M., Pendulation Suppression of a Shipboard Crane Using Fuzzy Controller, Proc. “Am. Control Conf. (ACC'99)”, San Diego, Califomia, 2-4 June 1999, pp. 586–590.

  105. Kiss, I.Z., Gáaspáar, V., and Hudson, J.L., Experiments on Synchronization and Control of Chaos on Coupled Electrochemical Oscillators, J. Phys. Chem. B, 2000, vol. 104, pp. 7554–7560.

    Google Scholar 

  106. Kiss, I.Z. and Gáaspáar, V., Controlling Chaos with Artificial Neural Network: Numerical Studies and Experiments, J. Phys. Chem. A, 2000, vol. 104, pp. 8033–8037.

    Google Scholar 

  107. Kiss, I.Z., Wang, W., and Hudson, J.L., Forcing, Coupling, and Feedback of Chaotic Electrochemical Oscillators, in Experimental Chaos, 6th Experimental Chaos Conf., Potsdam, Germany, 2001, AIP Conf. Proc., Boccaletti, S., Gluckman, B.J., Kurths, J., et al., Eds., New York, 2002, vol. 622, pp. 3–11.

  108. Klotz, A. and Brauer, K., A Small-Size Neural Network for Computing with Strange Attractors, Neural Netw., 1999, vol. 12, pp. 601–607.

    Google Scholar 

  109. Kocarev, L. and Parlitz, U., Genreal Approach for Chaotic Synchronization with Applications to Telecommunication, Phys. Rev. Lett., 1995, vol. 74, no. 25, pp. 5028–5031.

    Google Scholar 

  110. Kol'tsova, E.M., Gordeev, L.S., Korchagin, E.Y., et al., Control of Chaos in Chemical Systems (for the Process of Crystallization as an Example), Rus. J. Phys. Chemistry, 2000, vol. 74.

  111. Kol'tsova, E.M., Cherenkov, M.V., and Korchagin, E.Y., Non-linear Processes and Control of Chaos in Chemical Technology, in Proc. 2003 Int. Conf. “Physics and Control”, Fradkov, A.L. and Churilov, A.N., Eds., St. Petersburg, Russia, 2003, pp. 484–490.

  112. Kolumban, G., Kennedy, M.P., and Chua, L.O., The Role of Synchronization in Digital Communications Using Chaos. I. Fundamentals of Digital Communications, IEEE Trans. Circ. Syst., part I, 1997, vol. 44, no. 10, pp. 927–936; II. Chaotic Modulation and Chaotic Synchronization, IEEE Trans. Circ. Syst., part I, 1998, vol. 45, no. 11, pp. 1129–1140.

    Google Scholar 

  113. Kouomou, Y.C. and Woafo, P., Stability and Chaos Control in Electrostatic Transducers, Physica Scripta, 2000, vol. 62, pp. 255–260.

    Google Scholar 

  114. Lai, Y.C., Encoding Digital Information Using Transient Chaos, Int. J. Bifurcat. Chaos, 2000, vol. 10, pp. 787–795.

    Google Scholar 

  115. Lai, Y.M., Tse, C.K., and Chow, M.H.L., Control of Bifurcation in Current-Programmed DC/DC Converters: An Alternative Viewpoint of Ramp Compensation, Circuits Syst. Signal Process., 2001, vol. 20, pp. 695–707.

    Google Scholar 

  116. Lanchares, V., Iñarrea, M., and Salas, J.P., Spin Rotor Stabilization of a Dual-Spin Spacecraft with Time Dependent Moments of Inertia, Int. J. Bifurc. Chaos, 1998, vol. 8, no. 3, pp. 609–617.

    Google Scholar 

  117. Lee, S.T.S, Chung, H.S.H., Chen, G., and Hui, S.Y.R., Use of Chaotic Switching in Electronic Ballasts, PAPER Special Section on Nonlinear Theory and Its Applications.

  118. Lenci, S. and Rega, G., A Procedure for Reducing the Chaotic Response Region in an Impact Mechanical System, Nonlin. Dynam., 1998, vol. 15, pp. 391–409.

    Google Scholar 

  119. Lenci, S. and Rega, G., Controlling Nonlinear Dynamics in a Two-Well Impact System. I. Attractors and Bifurcation Scenario under Symmetric Excitations, Int. J. Bifurcat. Chaos, vol. 8, pp. 2387–2407.

  120. Lenci, S. and Rega, G., Numerical Control of Impact Dynamics Inverted Pendulum through Optimal Feedback Strategies, J. Sound Vibr., 2000, vol. 236, pp. 505–527.

    Google Scholar 

  121. Liao, T.-L. and Huang, N.-S., An Observer-based Approach for Chaotic Synchronization with Applications to Secure Communications, IEEE Trans. Circ. Syst. I, 1999, vol. 46, pp. 1144–1150.

    Google Scholar 

  122. Lim, T.K., Kwak, K., and Yun, M., An Experimental Study of Storing Information in a Controlled Chaotic System with Time-Delayed Feedback, Physics Letters A, 1998, vol. 240, pp. 287–294.

    Google Scholar 

  123. Locher, M., Johnson, G.A., and Hunt, E.R., Stability Analysis of Fixed Points via Chaos Control, Chaos, 1997, vol. 7, pp. 590–596.

    Google Scholar 

  124. Lorenz, H.W., Nonlinear Dynamical Equations and Chaotic Economy, Berlin: Springer, 1993.

    Google Scholar 

  125. Mariño, I.P., Rosa, E., Jr., and Grebogi, C., Exploiting the Natural Redundancy of Chaotic Signals in Communication Systems, Phys. Rev. Lett., 2000, vol. 85, no. 12, pp. 2629–2632.

    Google Scholar 

  126. Mariño, I.P., Lopez, L., and Sanjuan, M.A.F., Channel Coding in Communications Using Chaos, Physics Letters A, 2002, vol. 295, pp. 185–191.

    Google Scholar 

  127. Meehan, P.A. and Asokanthan, S.F., Control of Chaotic Instabilities in a Spinning Spacecraft with Dissipation Using Lyapunov Method, Chaos, Solitons, Fractals, 2002, vol. 13, pp. 1857–1869.

    Google Scholar 

  128. Meehan, P.A. and Asokanthan, S.F., Control of Chaotic Motion in a Dual-Spin Spacecraft with Nutational Damping, J. Guid., Control Dynam., 2002, vol. 25, no. 2, pp. 209–214.

    Google Scholar 

  129. Metcalf, G., Shinbrot, T., McCarthy, J.J., and Ottino, J.M., Avalanche Mixing of Granular Solids, Nature, 1995, vol. 374, pp. 39–41.

    Google Scholar 

  130. Mitsubori, K. and Aihara, K., Delayed-feedback Control of Chaotic Roll Motion of a Flooded Ship in Waves, Proc. R. Soc. London A, 2002, vol. 458, pp. 2801–2813.

    Google Scholar 

  131. Moon, F.C., Reddy, A.J., and Holmes, W.T., Experiments in Control and Anti-Control of Chaos in a Dry Friction Oscillator, J. Vibr. Control, 2003, vol. 9, pp. 387–397.

    Google Scholar 

  132. Morgül, Ö. and Solak, E., Observer Based Synchronization of Chaotic Systems, Phys. Rev., 1996, vol. E54, pp. 4803–4811.

    Google Scholar 

  133. Nijmeijer, H. and Mareels, I.M.Y., Observer Looks at Synchronization, IEEE Trans. Circ. Syst. I, 1997, vol. 44, no. 10, pp. 882–890.

    Google Scholar 

  134. Ott, E., Grebogi, C., and Yorke, J., Controlling Chaos, Phys. Revol. Lett., 1990, vol. 64, no. 11, pp. 1196–1199.

    Google Scholar 

  135. Ottino, J.M., The Kinematics of Mixing: Stretching, Chaos, and Transport, New York: Cambridge Univ. Press, 1989.

    Google Scholar 

  136. Parmananda, P., Madrigal, R., Rivera, M., Nyikos, L., Kiss, I.Z., and Gáspár, V., Stabilization of Unstable Steady States and Periodic Orbits in an Electrochemical System Using Delayed-Feedback Control, Phys. Revol. E, 1999, vol. 59, pp. 5266–5271.

    Google Scholar 

  137. Parmananda, P. and Eiswirth, M., Suppression of Chemical Turbulence Using Feedbacks and Forcing, J. Phys. Chem. A, 1999, vol. 103, pp. 5510–5514.

    Google Scholar 

  138. Parmananda, P., Rivera, M., Madrigal, R., Kiss, I.Z., and Gáspár, V., Resonant Control of Electrochemical Oscillations, J. Phys. Chem. B, 2000, vol. 104, pp. 11748–11751.

    Google Scholar 

  139. Paskota, M., Mees, A.I., Teo, K.L., Directing Orbits of Chaotic Systems in the Presence of Noise: Feedback Correction, Dynamics Control, 1997, vol. 7, pp. 25–47.

    Google Scholar 

  140. Paskota, M., On Modelling and the Control of Vibroformers in Aluminium Production, Chaos, Solitons, Fractals, 1998, vol. 9, pp. 323–335.

    Google Scholar 

  141. Paskota, M. and Lee, H.W.J., Targeting Moving Targets in Chaotic Dynamical Systems, Chaos, Solitons, Fractals, 1997, vol. 8, pp. 1533–1544.

    Google Scholar 

  142. Pecora, L.M., Carroll, T.L., Johnson, G.A., and Mar, D.J., Fundamentals of Synchronization in Chaotic Systems, Concepts and Applications, Chaos, 1997, vol. 7, no. 4, pp. 520–543.

    Google Scholar 

  143. Peil, M., Heil, T., Fischer, I., and Elesaber, W., Chaos-synchronization in Semiconductor Laser Systems: An Optical Phase Dependent Scenario, in AIP Conf. Proc.Experimental Chaos” 6th Experimental Chaos Conf., Potsdam, Germany, 2001, vol. 622, Boccaletti, S., Gluckman, B.J., Kurths, J., et al., Eds., New York, 2002, pp. 433–438.

  144. Peters, E., Chaos and Order in the Capital Markets, New York: Wiley, 1991.

    Google Scholar 

  145. Petrov, V., Bo Peng, and Showalter, K., A Map-Based Algorithm for Controlling Low-Dimensional Chaos, J. Chem. Phys., 1992, vol. 96, pp. 7506–7513.

    Google Scholar 

  146. Petrov, V., Gáspáar, V., Masere, J., and Showalter, K., Controlling Chaos in the Belousov-Zhabotinsky Reaction, Nature, 1993, vol. 361, pp. 240–243.

    Google Scholar 

  147. Petrov, V. and Showalter, K., Nonlinear Prediction, Filtering, and Control of Chemical Systems from Time Series, Chaos, 1997, vol. 7, pp. 614–620.

    Google Scholar 

  148. Piel, A., Greiner, F., Klinger, T., Krahnstover, N., and Mausbach, T., Chaos and Chaos Control in Plasmas, Physica Scripta, 2000, vol. T84, pp. 128–131.

    Google Scholar 

  149. Poddar, G., Chakrabarty, K., and Banerjee, S., Control of Chaos in DC-DC Converters, IEEE Trans. Circ. Syst. I., 1998, vol. 45, pp. 672–676.

    Google Scholar 

  150. Rappel, W.J., Fenton, F., and Karma, A., Spatiotemporal Control of Wave Instabilities in Cardiac Tissue, Phys. Rev. Lett., 1999, vol. 83, pp. 456–459.

    Google Scholar 

  151. Rem, B. and Armbruster, D., Control and Synchronization in Switched Arrival Systems, Chaos, 2003, vol. 13, no. 1, pp. 128–137.

    Google Scholar 

  152. Rosa, E., Jr., Hayes, S., and Grebogi, C., Noise Filtering in Communication with Chaos, Phys. Rev. Lett., 1997, vol. 78, no. 7, pp. 1247–1250.

    Google Scholar 

  153. Roy, R., Murphy, T.W., Maier, T.D., Gills, Z., and Hunt, E.R., Dynamical Control of a Chaotic Laser: Experimental Stabilization of a Globally Coupled System, Phys. Rev. Lett., 1992, vol. 68, pp. 1259–1262.

    Google Scholar 

  154. Chowdhury, R.A., Saha, P., and Banerjee, S., Control of Chaos in Laser Plasma Interaction, Chaos, Solitons, Fractals, 2002, vol. 12, pp. 2421–2426.

    Google Scholar 

  155. Rozman, M.G., Urbakh, M., and Klafter, J., Controlling Chaotic Frictional Forces, Phys. Revol. E, 1998, vol. 57, pp. 7340–7343.

    Google Scholar 

  156. Schöll, E., Amann, A., Schlesner, J., et al., Chaos Control of Nonlinear Current Oscillations in Semiconductor Heterostructures, in 2003 Int. Conf. “Physics and Control,” St. Petersburg, 2003 (http://www.rusycon.ru).

  157. Schomburg, E., Hofbeck, K., Scheuerer, R., et al., Control of the Dipole Domain Propagation in a Gaas/Alas Superlattice with a High-Frequency Field, Phys. Revol. B, 2002, vol. 65, p. 155320.

    Google Scholar 

  158. Sen, A.K., Control and Diagnostic Uses of Feedback, Physics of Plasmas, 2000, vol. 7, pp. 1759–1766.

    Google Scholar 

  159. Sharma, A. and Gupte, N., Control Methods for Problems of Mixing and Coherence in Chaotic Maps and Flows, PramanaJ. Physics, 1997, vol. 48, pp. 231–248.

    Google Scholar 

  160. Shinbrot, T., Alexander, A., and Muzzio, F.J., Spontaneous Chaotic Granular Mixing, Nature, 1999, vol. 397, no. 676.

  161. Sinha, S. and Ditto, W.L., Computing with Distributed Chaos, Phys. Revol. E, 1999, vol. 60, pp. 363–377.

    Google Scholar 

  162. Solé, R.V., Gamarra, J.G.P., Ginovart, M., and Lopez, D., Controlling Chaos in Ecology: From Deterministic to Individual-based Models, Bullet. Mathem. Biology, 1999, vol. 61, pp. 1187–1207.

    Google Scholar 

  163. Song, H., Li, Y.N., Chen, L., Cai, Z.S., Li, Y.J., Hou, Z., Zhao, X.Z., Controlling Belousov-Zhabotinsky-Continuous Stirred Tank Reactor Chaotic Chemical Reaction by Discrete and Continuous Control Strategies, PCCP Physical Chemistry Chemical Physics, 1999, vol. 1, pp. 813–819.

    Google Scholar 

  164. Sosnovtseva, O.V, Pavlov, A.N., Mosekilde, E., and Holstein-Rathlou, N.-H., Bimodal Dynamics in Nephron Autoregulation, in Proc. 2003 Int. Conf. “Physics and Control,” Fradkov, A.L. and Churilov, A.N., Eds., St. Petersburg, Russia, 2003, pp. 283–288.

  165. Srivastava, K.N. and Srivastava, S.C., Elimination of Dynamic Bifurcation and Chaos in Power Systems Using Facts Devices, IEEE Trans. Circ. Syst. I, 1998, vol. 45, pp. 72–78.

    Google Scholar 

  166. Srivastava, K.N. and Srivastava, S.C., Quasi-periodic Route to Chaos and Its Control in a Power-System Model, Eur. Trans. Electr. Power, 1999, vol. 9, pp. 241–245.

    Google Scholar 

  167. Suárez, I., Mastering Chaos in Ecology, Ecological Modelling, 1999, vol. 117, pp. 305–314.

    Google Scholar 

  168. Tang, S., Illing, L., Liu, J.M., et al., Communication Using Synchronization of Chaos Semiconductor Lasers with Optoelectronic Feedback, in Experimental Chaos. 6th Experimental Chaos Conf., Potsdam, Germany, 2001, Boccaletti, S., Gluckman, B.J., Kurths, J., et al., Eds., AIP Conf. Proc., New York, 2002, vol. 622, pp. 224–229.

  169. Thomas, K.I. and Ambika, G., Suppression of Smale Horseshoe Structure via Secondary Perturbations in Pendulum Systems, PramanaJ. Physics, 1999, vol. 52, pp. 375–387.

    Google Scholar 

  170. Tôrres, L.A.B. and Aguirre, L.A., Extended Chaos Control Method Applied to Chua Circuit, Electr. Lett., 1999, vol. 35, no. 10, pp. 768–770.

    Google Scholar 

  171. Uchida, A., Shinozuka, M., Kinugawas, S., et al., Chaotic On-Off Keying in Laser Systems for Optical Secure Communications, in Experimental Chaos. 6th Experimental Chaos Conf., Potsdam, Germany, 2001, AIP Conf. Proc., vol. 622, Boccaletti, S., Gluckman, B.J., Kurths, J., et al., Eds., New York, 2002, pp. 317–328.

  172. Vincent, T.L., Control Using Chaos, IEEE Contr. Syst. Magazine, 1997, vol. 17, pp. 65–76.

    Google Scholar 

  173. Vincent, T.L. and Mees, A.I., Controlling a Bouncing Ball, Int. J. Bifurcat. Chaos., 2000, vol. 10, pp. 579–592.

    Google Scholar 

  174. Wiener, R.J., Dolby, D.C., Gibbs, G.C., Squires, B., Olsen, T., and Smiley, A.M., Control of Chaotic Pattern Dynamics in Taylor Vortex Flow, Phys. Rev. Lett., 1999, vol. 83, pp. 2340–2343.

    Google Scholar 

  175. Wu, W., Nonlinear Bounded Control of a Nonisothermal CSTR, Industr. Eng. Chem. Research, 2000, vol. 39, pp. 3789–3798.

    Google Scholar 

  176. Xiao, J.H., Hu, G., and Gao, J.H., Turbulence Control and Synchronization and Controllable Pattern Formation, Int. J. Bifurcat. Chaos, 2000, vol. 10, pp. 655–660.

    Google Scholar 

  177. Yamapi, R., Chabi Orou, J.B., and Woafo, P., Harmonic Oscillations, Stability and Chaos Control in a Non-Linear Electromechanical System, J. Sound Vibr., 2003, vol. 259, no. 5, pp. 1253–1264.

    Google Scholar 

  178. Yang, T. and Chua, L.O., Chaotic Digital Code-Division Multiple Access (Cdma) Communication Systems, Int. J. Bifurcat. Chaos, 1997, vol. 7, pp. 2789–2805.

    Google Scholar 

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Andrievskii, B.R., Fradkov, A.L. Control of Chaos: Methods and Applications. II. Applications. Automation and Remote Control 65, 505–533 (2004). https://doi.org/10.1023/B:AURC.0000023528.59389.09

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