Control of Chaos: Survey 1997-2000

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 15, Issue 1, 2002, Pages 131-142

  Fradkov, Alexander L ^a   Evans, Robin J ^b  

^a INSTITUTE OF PROBLEMS OF MECHANICAL ENGINEERING   (Russian Federation)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Chaotic behavior; Nonlinear control

Indexed keywords

AUTOMATION; FEEDBACK LINEARIZATION; SURVEYS;

CHAOS CONTROL; CHAOTIC BEHAVIORS; CONTROL OF CHAOS; NON LINEAR CONTROL; PERIODIC EXCITATIONS; PYRAGAS; TIME DELAY FEEDBACKS; UNSOLVED PROBLEMS;

DELAY CONTROL SYSTEMS;

EID: 84945563592     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20020721-6-es-1901.01645     Document Type: Conference Paper

References (150)

1. Chen, G., and X. Dong, (1998A), From chaos to order: perspectives, methodologies and applications, World Scientific, Singapore.
2. Fradkov, A.L. and Pogromsky, A. Yu. (1998A) Introduction to control of oscillations and chaos. World Scientific, Singapore.
3. Handbook of Chaos Control (1999 A). /Ed. H.G. Schuster, Wiley & Sons.
4. Controlling Chaos and Bifurcations in Engineering Systems (1999A). /Ed. G. Chen, CRC Press.
5. Coping with Chaos (1994A). /Eds. Ott E., Sauer T., Yorke J. New York: Wiley.
6. Kapitanyak T. (1996A). Controlling Chaos. New York: Academic Press.
7. Boccaletti, S, Grebogi, C, Lai, YC, Mancini, H, Maza, D (2000A) The control of chaos: theory and applications. Physics Reports, V. 329, 2000, 103-197.
8. Arecchi, FT, Boccaletti, S, Ciofini, M, Meucci, R, Grebogi, C (1998A) The control of chaos: Theoretical schemes and experimental realizations Intern. J. Bifurcation and Chaos, V. 8, 1998, 1643-1655.
9. Ding, MZ, Ding, EJ, Ditto, WL, Gluckman, B, In, V, Peng, JH, Spano, ML, Yang, WM Control and synchronization of chaos in high dimensional systems: Review of some recent results. Chaos, V. 7, 1997, 644-652.
10. Sharma, A, Gupte, N Control methods for problems of mixing and coherence in chaotic maps and flows. Pramana - J. of Physics, V. 48, 1997, 231-248.
11. Gadre, SD, Varma, VS Control of chaos. Pramana - J. of Physics, V. 48, 1997, 259-270.
12. Alekseev, V.V. and A. Y. Loskutov, (1987), Control of a system with a strange attractor through periodic parametric action, Sov. Phys. Dokl., Vol. 32, 1346-1348.
13. Basios, V, Bountis, T, Nicolis, G Controlling the onset of homoclinic chaos due to parametric noise Phys. Let. A, V. 251, 1999, 250-258.
14. Bellman R., Bentsman J., Meerkov S. Vibrational control of nonlinear systems. IEEE Trans. Aut. Contr. 1986. V. AC-31. no 8, 710-724.
15. Belhaq, M, Houssni, M Suppression of chaos in averaged oscillator driven by external and parametric excitations. Chaos, Solitons & Fractals, V. 11, 2000, 1237-1246.
16. Blekhman, I., (2000), Vibrational Mechanics, World Scientific, Singapore, (in Russian: 1994).
17. Bogoliubov, N.N. and Yu.A. Mitropolski (1961) Asymptotic Methods in the Theory of Nonlinear Oscillations, New-York, Gordon-Breach.
18. Chizhevsky, VN, Vilaseca, R, Corbalan, R Experimental switchings in bistability domains induced by resonant perturbations. Intern. J. Bifurcation and Chaos, V. 8, 1998, 1777-1782.
19. Dykstra, R, Rayner, A, Tang, DY, Heckenberg, N.R. (1998) Experimentally tracking unstable steady states by large periodic modulation Phys. Rev. E, V. 57, 1998, 397-401.
20. Fronzoni, L, Giocondo, and M. Pettini (1991) Experimental evidence of suppression of chaos by resonant parametric perturbations. Phys. Rev. A, V. 43, 6483-6487.
21. Genesio R., Tesi A., (1992) Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems. Automatica, V. 28, no 3, 531-548.
22. Hsu, R.R., Su, H.T, Chern, J.L, Chen, C.C. (1997) Conditions to control chaotic dynamics by weak periodic perturbation Phys. Rev. Let. V. 78, 1997, 2936-2939.
23. Hubler A. and E. Lusher (1989) Resonant stimulation and control of nonlinear oscillators. Naturwissenschaft, V. 76, 67-71.
24. Kapitsa P.L. (1951) Dynamic stability of a pendulum with oscillating suspension point. Zh. Exper. Teor. Phys. v. 21, No 5.
25. Kul'minskii, A, Vilaseca, R, Corbalan, R (2000) Tracking unstable steady states by large-amplitude low-frequency periodic modulation of a control parameter: Phase-space analysis Phys. Rev. E, V. 61, (3), 2500-2505.
26. Leonov, G.A., I.M. Burkin and A.I. Shepelyavyi, (1995), Frequency Methods in Oscillation Theory, (Kluwer, Dordrecht), (in Russian: 1992).
27. Leonov, G.A., D.V. Ponomarenko and V.B. Smirnova, (1996), Frequency Methods for Nonlinear Analysis. Theory and Applications, World Scientific, Singapore.
28. Lima, R, Pettini, M (1990) Suppression of chaos by resonant parametric perturbations. Phys. Rev. A., V. 41, pp. 726-733.
29. Lima, R, Pettini, M (1998) Parametric resonant control of chaos. Intern. J. Bifurcation and Chaos, V. 8, 1675-1684.
30. Matsumoto K., and Tsyda I., (1983) Noise induced order. J. Stat. Phys., v. 31, pp. 87-106.
31. Meerkov S.M. Principle of vibrational control: theory and applications. IEEE Trans. Aut. Contr. 1980. V. AC-25, 755-762.
32. Mettin, R Control of chaotic maps by optimized periodic inputs. Intern. J. Bifurcation and Chaos, V. 8, 1998, 1707-1711.
33. Mirus, KA, Sprott, JC Controlling chaos in low- and high-dimensional systems with periodic parametric perturbations. Phys. Rev. E, V. 59, 1999, 5313-5324.
34. Morgul, O On the control of chaotic systems in Lur'e form by using dither. IEEE Trans. Circ. Syst. I, V. 46, 1999, 1301-1305.
35. Peles, S Analysis of periodically driven mechanical system. Progress of Theor. Physics Supplement, V., 2000, 496-506.
36. Pettini M. (1988) Controlling chaos through parametric excitations In: Dynamics and Stochastic Processes, eds. Lima R., Streit L., & Vilela-Mendes, R.V. Springer-Verlag, NY, pp. 242-250.
37. Pisarchik, AN, Corbalan, R Parametric nonfeedback resonance in period doubling systems Phys. Rev. E, V. 59, 1999, 1669-1674.
38. Piskun, NY, Wigen, PE Bifurcation to chaos in auto-oscillations in circular yttrium-ion-garnet films. J. of Appl. Phys., V. 85, 1999, 4521-4523.
39. Rajasekar, S, Murali, K, Lakshmanan, M Control of chaos by nonfeedback methods in a simple electronic circuit system and the FitzHugh-Nagumo equation. Chaos, Solitons & Fractals, V. 8, 1997, 1545-1558.
40. Ramesh, M, Narayanan, S Chaos control by nonfeedback methods in the presence of noise. Chaos, Solitons & Fractals, V. 10, 1999, 1473-1489.
41. Simiu, E, Franaszek, M Melnikov-based open-loop control of escape for a class of nonlinear systems. J. of Dynamic Systems Measur. Contr., Trans. ASME, V. 119, 1997, 590-594.
42. Stephenson A. On a new type of dynamical stability, (1908) Mem. Proc. Manch. Lit. Phil. Soc. 52, 1-10
43. On induced stability," Phil. Mag. 15, 233-236.
44. Tereshko V, Shchekinova, E. Resonant control of the Rossler system. Phys. Rev E, 1998, V. 58, 423-426.
45. Zames G. and N.A. Shneydor. Dither in nonlinear systems. IEEE Trans. Autom. Contr., V. 21, (1976), 660-667.
46. Zhalnin, AY Control of chaos in nonautonomous systems with quasiperiodic excitation. Techn. Phys. Let., V. 25, 1999, 662-664.
47. Agiza, HN On the analysis of stability, bifurcation, chaos and chaos control of Kopel map. Chaos, Solitons & Fractals, V. 10, 1999, 1909-1916.
48. Aston, PJ, Bird, CM Analysis of the control of chaos - Extending the basin of attraction Chaos, Solitons & Fractals, V. 8, 1997, 1413-1429.
49. Aston, PJ, Bird, CM Using control of chaos to refine approximations to periodic points. Intern. J. of Bifurcation and Chaos, V. 10, 2000, 227-235.
50. Badescu, CS, Ignat, M, Oprisan, S On the chaotic oscillations of Bloch walls and their control. Chaos, Solitons & Fractals, V. 8, 1997, 33-43.
51. Bezruchko, BP, Ivanov, RN, Ponomarenko, VI Two-level control of chaos in nonlinear oscillators. Techn. Phys. Let., V. 25, 1999, 151-153.
52. Braun, T Suppression and excitation of chaos: The example of the glow discharge. Intern. J. of Bifurcation and Chaos, V. 8, 1998, 1739-1742.
53. Chanfreau, P, Lyyjynen, H Viewing the efficiency of chaos control. J. of Nonlin. Math. Physics, V. 6, 1999, 314-331.
54. Epureanu, BI, Dowell, EH System identification for the Ott-Grebogi-Yorke controller design. Phys. Rev. E, V. 56, 1997, 5327-5331.
55. Epureanu, BI, Dowell, EH On the optimality of the Ott-Grebogi-Yorke control scheme. Physica D, V. 116, 1998, 1-7.
56. Epureanu, BI, Dowell, EH Optimal multi-dimensional OGY controller. Physica D, V. 139, 2000, 87-96.
57. Flynn, C, Wilson, N A simple method for controlling chaos. American J. of Physics, V. 66, 1998, 730-735.
58. Fradkov, A.L. and P. Yu. Guzenko, (1997), Adaptive control of oscillatory and chaotic systems based on linearization of Poincaré map. Proc. 4th Europ. Contr. Conf. Brussels, 1-4 July.
59. Fradkov, A.L., P. Yu. Guzenko and A.V. Pavlov, (1998), Adaptive control of chaotic systems based on Poincaré map and controlled closing lemma. IFAC NOLCOS'98, Twente, The Netherlands, 739-744.
60. Fradkov, A, Guzenko, P, Pavlov, A Adaptive control of recurrent trajectories based on linearization of Poincare map. Intern. J. of Bifurcation and Chaos, V. 10, 2000, 621-637.
61. Grebogi, C, Lai, YC Controlling chaos in high dimensions IEEE Trans. Circ. Syst. I, V. 44, 1997, 971-975.
62. Grebogi, C, Lai, YC Controlling chaotic dynamical systems. Syst. & Contr. Letters, V. 31, 1997, 307-312.
63. Grebogi, C, Lai, YC, Hayes, S Control and applications of chaos. Intern. J. of Bifurcation and Chaos, V. 7, 1997, 2175-2197.
64. Grebogi, C, Lai, YC, Hayes, S Control and applications of chaos. J. Franklin Inst. - Eng. and Appl. Math., V. 334B, 1997, 1115-1146.
65. Holzhuter, T, Klinker, T Control of a chaotic relay system using the OGY method. Zeitschrift Fur Natur-forschung Section AMA J. of Phys. Sciences, V. 53, 1998, 1029-1036.
66. Holzhuter, T, Klinker, T Transient behavior for one-dimensional OGY control. Intern. J. of Bifurcation and Chaos, V. 10, 2000, 1423-1435.
67. Hunt, E.R., (1991), Stabilizing high-period orbits in a chaotic system - the diode resonator, Phys. Rev. Lett., 67, pp. 1953-1955.
68. Obradovic, D, Lenz, H When is OGY control more than just pole placement. Intern. J. of Bifurcation and Chaos, V. 7, 1997, 691-699.
69. Okuno, H, Sakata, T, Takeda, H Controlling chaos of nonlinear domain-wall motion. J. of Appl. Physics, V. 85, 1999, 5083-5085.
70. Ott, E., C. Grebogi, and J. Yorke, (1990), Controlling chaos. Phys. Rev. Lett., Vol. 64(11), 1196-1199.
71. Ritz, T, Schweinsberg, ASZ, Dressler, U, Doerner, R, Hubinger, B, Martienssen, W Chaos control with adjustable control times. Chaos, Solitons & Fractals, V. 8, 1997, 1559-1576.
72. Senesac, LR, Blass, WE, Chin, G, Hillman, JJ, Lobell, JV Controlling chaotic systems with occasional proportional feedback. Review of Scientific Instruments, V. 70, 1999, 1719-1724.
73. Schweinsberg, ASZ, Ritz, T, Dressier, U, Hubinger, B, Doerner, R, Martienssen, W Quasicontinuous control of a bronze ribbon experiment using time-delay coordinates. Phys. Rev. E, V. 55, 1997, 2145-2158.
74. Yang, L, Liu, ZG An improvement and proof of OGY method. Applied Mathematics and Mechanics: English Edition, V. 19, 1998, 1-8.
75. Zhao, H, Wang, YH, Zhang, ZB Extended pole placement technique and its applications for targeting unstable periodic orbit Phys. Rev. E, V. 57, 1998, 5358-5365.
76. Basso, M, Genesio, R, Tesi, A Stabilizing periodic orbits of forced systems via generalized Pyragas controllers IEEE Trans. Circ. Syst. I, V. 44, 1997, 1023-1027.
77. Basso, M, Genesio, R, Giovanardi, L, Tesi, A, Torrini, G On optimal stabilization of periodic orbits via time delayed feedback control. Intern. J. of Bifurcation and Chaos, V. 8, 1998, 1699-1706.
78. Batlle, C, Fossas, E, Olivar, G Stabilization of periodic orbits of the buck converter by time-delayed feedback, Intern. J. Circ. Theory and Appl., V. 27, 1999, 617-631.
79. Bleich, ME, Hochheiser, D, Moloney, JV, Socolar, JES Controlling extended systems with spatially filtered, time-delayed feedback. Phys. Rev. E, V. 55, 1997, 2119-2126.
80. Brandt, ME, Shih, HT, Chen, GR Linear time-delay feedback control of a pathological rhythm in a cardiac conduction model. Phys. Rev. E, V. 56, 1997, R1334-R1337.
81. Chen, GR, Yu, XH On time-delayed feedback control of chaotic systems. IEEE Trans. Circ. Syst. I, V. 46, 1999, 767-772.
82. Elmer, FJ Controlling friction Phys. Rev. E, V. 57, 1998, R4903-R4906.
83. Hai, WH, Duan, YW, Pan, LX An analytical study for controlling unstable periodic motion in magneto-elastic chaos. Phys. Lett. A, V. 234, 1997, 198-204.
84. Hikihara, T, Touno, M, Kawagoshi, T Experimental stabilization of unstable periodic orbit in magneto-elastic chaos by delayed feedback control. Intern. J. Bifurcation Chaos, V. 7, 1997, 2837-2846.
85. Just, W, Bernard, T, Ostheimer, M, Reibold, E, Benner, H Mechanism of time-delayed feedback control. Phys. Rev. Lett., V. 78, 1997, 203-206.
86. Just, W, Reibold, E, Benner, H, Kacperski, K, Fronczak, P, Holyst, J Limits of time-delayed feedback control. Physics Letters A, V. 254, 1999, 158-164.
87. Just, W, Reibold, E, Kacperski, K, Fronczak, P, Holyst, JA, Benner, H Influence of stable Floquet exponents on time-delayed feedback control. Phys. Rev. E, V. 61, 2000, 5045-5056.
88. Konishi, K, Kokame, H Observer-based delayed-feedback control for discrete-time chaotic systems. Phys. Lett. A, V. 248, 1998, 359-368.
89. Konishi, K, Hirai, M, Kokame, H Decentralized delayed-feedback control of a coupled map model for open flow. Phys. Rev. E, V. 58, 1998, 3055-3059.
90. Konishi, K, Kokame, H, Hirata, K Coupled map car-following model and its delayed-feedback control. Phys. Rev. E, V. 60, 1999, 4000-4007.
91. Konishi, K, Kokame, H, Hirata, K Decentralized delayed-feedback control of a coupled ring map lattice. IEEE Transactions On Circuits And Systems I. Fundamental Theory And Applications, V. 47, 2000, 1100-1102.
92. Konishi, K, Kokame, H, Hirata, K Delayed-feedback control of spatial bifurcations and chaos in open-flow models. Phys. Rev. E, V. 62, 2000, 384-388.
93. Konishi, K, Kokame, H, Hirata, K Decentralized delayed-feedback control of an optimal velocity traffic model. European Phys. J. B, V. 15, 2000, 715-722.
94. Loiko, NA, Naumenko, AV, Turovets, SI Effect of Pyragas feedback on the dynamics of a Q-switched laser. J. Exper. Theor. Physics, V. 85, 1997, 827-834.
95. Nakajima, H On analytical properties of delayed feedback control of chaos. Phys. Lett. A, V. 232, 1997, 207-210.
96. Nakajima, H, Ueda, Y Half-period delayed feedback control for dynamical systems with symmetries. Phys. Rev. E, V. 58, 1998, 1757-1763.
97. Nakajima, H, Ueda, Y Limitation of generalized delayed feedback control. Physica D, V. 111, 1998, 143-150.
98. Pyragas K. (1992) Continuous control of chaos by self-controlling feedback. Phys. Lett. A., Vol. 170, 421-428.
99. Quyen, MLV, Martinerie, J, Adam, C, Varela, FJ Unstable periodic orbits in human epileptic activity. Phys. Rev. E, V. 56, 1997, 3401-3411.
100. Simmendinger, C, Hess, O, Wunderlin, A Analytical treatment of delayed feedback control. Phys. Lett. A, V. 245, 1998, 253-258.
101. Abarbanel, HDI, Korzinov, L, Mees, AI, Starobinets, IM Optimal control of nonlinear systems to given orbits. Syst. & Contr. Lett., V. 31, 1997, 263-276.
102. Abarbanel, HDI, Korzinov, L, Mees, AI, Rulkov, NF Small force control of nonlinear systems to given orbits. IEEE Trans. Circ. Syst. I, V. 44, 1997, 1018-1023.
103. Caranicolas, ND Controlling chaos in map models. Mechanics Research Communications, V. 26, 1999, 13-20.
104. Codreanu, S, Danca, M Suppression of chaos in a one-dimensional mapping. J. of Biol. Physics, V. 23, 1997, 1-9.
105. Gonzalez, J, Femat, R, Alvarez-Ramirez, J, Aguilar, R, Barron, M A discrete approach to the control and synchronization of a class of chaotic oscillators. IEEE Trans. Circ. Syst. I, V. 46, 1999, 1139-1144.
106. Guzenko, P. Yu and A.L. Fradkov, (1997), Gradient control of Hénon map dynamics. Intern. J. of Bifurcation and Chaos, Vol. 7 (3), 701-705.
107. Escalona, J, Parmananda, P Noise-aided control of chaotic dynamics in a logistic map. Phys. Rev. E, V. 61, 2000, 5987-5989.
108. Hill, DL Control of implicit chaotic maps using nonlinear approximations. Chaos, V. 10, 2000, 676-681.
109. Imamori, T, Ushio, T Discrete-time Hogg-Huberman strategy with net bias. Electronics and Communications in Japan, Part III - Fundamental Electronic Science, V. 83, 2000, 31-37.
110. Konishi, K, Kokame, H Observer-based delayed-feedback control for discrete-time chaotic systems. Phys. Lett. A, V. 248, 1998, 359-368.
111. Kwon, OJ Targeting and stabilizing chaotic trajectories in the standard map. Phys. Lett. A, V. 258, 1999, 229-236.
112. Lee, HWJ, Paskota, M, Teo, KL Mixed strategy global sub-optimal feedback control for chaotic systems. Intern. J. Bifurcation and Chaos, V. 7, 1997, 607-623
113. Lenz, H, Obradovic, D Stabilizing higher periodic orbits of chaotic discrete-time maps. Intern. J. Bifurcation and Chaos, V. 9, 1999, 251-266.
114. Levi, P, Schanz, M, Kornienko, S, Komienko, O Application of order parameter equations for the analysis and the control of nonlinear time discrete dynamical systems. Intern. J. Bifurcation and Chaos, V. 9, 1999, 1619-1634.
115. Liao, TL, Huang, NS Control and synchronization of discrete-time chaotic systems via variable structure control technique. Phys. Lett. A, V. 234, 1997, 262-268.
116. McGuire, J, Batchelor, MT, Davies, B Linear and optimal non-linear control of one-dimensional maps. Phys. Lett. A, V. 233, 1997, 361-364.
117. Melby, P, Kaidel, J, Weber, N, Hubler, A Adaptation to the edge of chaos in the self-adjusting logistic map. Phys. Rev. Lett., V. 84, 2000, 5991-5993.
118. Mettin, R Control of chaotic maps by optimized periodic inputs. Intern. J. Bifurcation and Chaos, V. 8, 1998, 1707-1711.
119. Park, KS, Park, JB, Choi, YH, Yoon, TS, Chen, GR Generalized predictive control of discrete-time chaotic systems. Intern. J. Bifurcation and Chaos, V. 8, 1998, 1591-1597.
120. Place, CM, Arrowsmith, DK Control of transient chaos in tent maps near crisis. Phys. Rev. E, V. 61, 2000, 1: 1357-1368, 11: 1369-1381.
121. Yang, T, Chua, LO Control of chaos using sampled-data feedback control. Intern. J. Bifurcation and Chaos, V. 8, 1998, 2433-2438.
122. Alleyne, A Reachability of chaotic dynamic systems. Phys. Rev. Lett., V. 80, 1998, 3751-3754.
123. Chen, GR On some controllability conditions for chaotic dynamics control. Chaos, Solitons & Fractals, V. 8, 1997, 1461-1470.
124. Lions, JL. On the controllability of distributed systems. Proc. Nat. Acad. Sci. USA, V. 94, No 10, (1997), 4828-4835.
125. Van de Vorst, ELB, Kant, AR, Van de Molengraft, MJG, Kok, JJ, Van Campen, DH Stabilization of periodic solutions of nonlinear mechanical systems: Controllability and stability. J. of Vibration and Control, V. 4, 1998, 277-296.
126. Kousaka, T, Ueta, T, Kawakami, H A method for generating a chaotic attractor by destabilization. Electronics and Communications in Japan, Part III - Fundamental Electronic Science, V. 80, 1997, 73-81.
127. Postnikov, NS Stochasticity of relay systems with hysteresis. Automat. Remote Contr., V. 59, 1998, 349-358.
128. Vanecek A., Celikovsky S. Chaos synthesis via root locus. IEEE Trans. Circ. Syst. I, V. 41, 1994, 59-60.
129. Wang, XF, Chen, GR Chaotifying a stable LTI system by tiny feedback control. IEEE Trans. Circ. Syst. I, V. 47, 2000, 410-415.
130. Wang, XF, Chen, GR Chaotification via arbitrarily small feedback controls: Theory, method, and applications. International Journal Of Bifurcation And Chaos, V. 10, 2000, 549-570.
131. Antoniou, I., Bosco, F. Probabilistic control of chaos through small perturbations. Chaos, Solitons, Fractals, V. 11, (2000), No 1-3, 359-371.
132. Bollt, EM Controlling chaos and the inverse Frobenius-Perron problem: Global stabilization of arbitrary invariant measures. Int. J. Bifurcation Chaos, V. 10 (2000), no 5, 1033-1050.
133. Gora, P Boyarsky, A A new approach to controlling chaotic systems. Physica D, V. 111 (1998), No 1-4, 1-15.
134. Fouladi, A, Valdivia, JA Period control of chaotic systems by optimization. Phys. Rev. E, V. 55, 1997, 1315-1320.
135. Park J., Kim J., Cho S.H., Han K.H., Yi CK, Jin G.T. Development of sorbent manufacturing technology by agitation fluidized bed granulator. Korean J. Chem. Eng. v. 16 (1999), No 5, 659-663.
136. Ravindra, B, Hagedorn, P Invariants of chaotic attractor in a nonlinearly damped system. J. of Applied Mechanics-Trans. ASME, V. 65, 1998, 875-879.
137. Schwartz I.B. and I. Triandaf, Tracking unstable orbits in experiments: A new continuation method, Phys. Rev. A, 46, pp. 7439-7444, 1992.
138. Schwartz, LB, Carr, TW, Triandaf, I Tracking controlled chaos: Theoretical foundations and applications Chaos, V. 7, 1997, 664-679.
139. Schwartz I.B. and Triandaf I. Tracking sustained chaos. Intern. J. Bifurcation Chaos, V. 10 (2000), 571-578.
140. Huijberts, H, Nijmeijer, H., Willems, R System identification in communication with chaotic systems IEEE Trans. Circ. Syst. I, V. 47 (2000) no 6, 800-808.
141. Maybhate, A, Amritkar, RE Dynamic algorithm for parameter estimation and its applications. Phys. Rev. E, V. 61, 2000, 6461-6470.
142. Petrick, MH, Wigdorowitz, B A priori nonlinear model structure selection for system identification. Control Eng. Practice, V. 5, 1997, 1053-1062.
143. Poznyak, AS Yu, W Sanchez, EN Identification and control of unknown chaotic systems via dynamic neural networks. IEEE Trans. Circ. Syst. I, V. 46 (1999), no 12, 1491-1495.
144. Alvarez, J, Curiel, E, Verduzco, F Complex dynamics in classical control systems Syst. & Contr. Lett., V. 31, 1997, 277-285.
145. J. Baillieul, R. W. Brockett and R. B. Washburn. Chaotic motion in nonlinear feedback systems. IEEE Trans. Circ. Syst. I, 27, pp. 990-997, 1980.
146. Enikov, E, Stepan, G Microchaotic motion of digitally controlled machines. Journal of Vibration and Control, V. 4, 1998, 427-443.
147. Gray, GL, Mazzoleni, AP, Campbell, DR Analytical criterion for chaotic dynamics in flexible satellites with nonlinear controller damping. J. of Guidance, Contr. Dynamics, V. 21, 1998, 558-565.
148. Mackey M.C., Glass L. Oscillation and chaos in physiological control systems. Science, 197 (1977) 287-280.
149. Mareels I.M.Y. and Bitmead R.R. Non-linear dynamics in adaptive control: chaotic and periodic stabilization. Automatica, I: V. 22, (1986), 641-655; II: V. 24, (1988), 485-497.
150. Vincent, TL Control using chaos. IEEE Contr. Syst. Magazine, V. 17, 1997, 65-76.