Method of passification in adaptive control, estimation, and synchronization

Automation and Remote Control

Volumn 67, Issue 11, 2006, Pages 1699-1731

  Andrievskii, B R ^a   Fradkov, A L ^a  

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

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE ALGORITHMS; FEEDBACK; OSCILLATORS (ELECTRONIC); PARAMETER ESTIMATION; SYNCHRONIZATION; THEOREM PROVING;

ADAPTIVE CONTROL STATE ESTIMATION; ADAPTIVE TUNING; CHAOTIC SIGNALS; SIGNAL-PARAMETRIC ALGORITHMS;

ADAPTIVE CONTROL SYSTEMS;

EID: 33751539277     PISSN: 00051179     EISSN: None     Source Type: Journal    
DOI: 10.1134/S0005117906110014     Document Type: Article

References (97)

1. Bogolyubov, N.N. and Mitropol'skii, Yu.A., Asimptoticheskie metody v teorii nelineinykh kolebanii (Asymptotic Methods in the Theory of Nonlinear Oscillations), Moscow: Nauka, 1974.
2. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal'nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Nauka, 1974.
3. Kharitonov, V.L., On Asymptotical Stability of the Equilibrium of the Systems of Linear Differential Equations, Diff. Uravn., 1978, vol. 11, pp. 2086-2088.
4. Matveev, A.S., Theory of Optimal Control in the Works of V.A. Yakubovich, Avtom. Telemekh., 2006, no. 10, pp. 120-174.
5. Gusev, S.V. and Likhtarnikov, A.L., Kalman-Popov-Yakubovich Lemma and the S-procedure: A Historical Essay, Avtom. Telemekh., 2006, no. 11, pp. 77-121.
6. Barabanov, N.E., Gelig, A.Kh., Leonov, G.A., et al., Frequency Theorem (Yakubovich-Kalman Lemma) in the Control Theory, Avtom. Telemekh., 1996, no. 10, pp. 3-40.
7. Petrov, B.N., Rutkovskii, V.Yu., Krutova, I.N., and Zemlyakov, S.D., Printsipy postroeniya i proektirovaniya samonastraivayushchikhsya sistem (Principles of Construction and Design of the Self-adjusting Systems), Moscow: Mashinostroenie, 1972.
8. Yakubovich, V.A., Solution of some Matrix Inequalities in the Automatic Control Theory, Dokl. Akad. Nauk SSSR, 1962, vol. 143, no. 6, pp. 1304-1307.
9. Translated into English as: The Solution of Certain Matrix Inequalities in Automatic Control Theory, Soviet Math. Dokl., 1962, no. 3, pp. 620-623.
10. Toker, O. and Ozbay, H., On the NP-hardness of Solving Bilinear Matrix Inequalities and Simultaneous Stabilization with Static Output Feedback, in Proc. Am. Control Conf., 1995, pp. 2525, 2526.
11. Fradkov, A.L., Design of an Adaptive System of Stabilization of a Linear Dynamic Plant, Avtom. Telemekh., 1974, no. 12, pp. 96-103.
12. Fradkov, A.L., Quadratic Lyapunov Functions in the Problem of Adaptive Stabilization of the Linear Dynamic Plant, Sib. Mat. Zh., 1976, vol. 17, no. 2, pp. 436-445.
13. Translated into English in Siberian Math. J., 1976, vol. 17, no. 2, pp. 341-348.
14. Seron, M.M., Hill, D.J., and Fradkov, A.L., Adaptive Passification of Nonlinear Systems, in Proc. 33rd Conf. Dec. Control, CDC, 1994, pp. 190-195.
15. Fomin, V.N., Fradkov, A.L., and Yakubovich, V.A., Adaptivnoe upravlenie dinamicheskimi ob"ektami (Adaptive Control of Dynamic Plants), Moscow: Nauka, 1981.
16. Fradkov, A.L., Adaptivnoe upravlenie slozhnymi sistemami (Adaptive Control of Complex Systems), Moscow: Nauka, 1990.
17. Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nelininoe i adaptivnoe upravlenie slozhnymi sistemami (Nonlinear and Adaptive Control of Complex Systems), St. Petersburg: Nauka, 2000.
18. Translated into English under the title Nonlinear and Adaptive Control of Complex Systems, Dordrecht: Kluwer, 1999.
19. Andrievskii, B.R., Stotskii, A.A., and Fradkov, A.L., Algorithms of the Speed Gradient in Adaptation and Control, Avtom. Telemekh., 1988, no. 12, pp. 3-39.
20. Andrievsky, B.R. and Fradkov, A.L., Adaptive Controllers with Implicit Reference Models Based on Feedback Kalman-Yakubovich Lemma, in Proc. 3rd IEEE Conf. Control Appl., Glasgow, 1994, pp. 1171-1174.
21. Andrievsky, B.R., Churilov, A.N., and Fradkov, A.L., Feedback Kalman-Yakubovich Lemma and Its Applications to Adaptive Control, in Proc. 35th IEEE Conf. Dec. Control, Kobe, 1996.
22. Andrievskii, B.R. and Fradkov, A.L., Izbrannye glavy teorii avtomaticheskogo upravleniya s primerami na yazyke MATLAB (Selected Chapters of the Theory of Automatic Control with Examples in MATLAB), St. Petersburg: Nauka, 1999.
23. Popov, V.M., On One Problem in the Theory of Absolute Stability of Automatic Systems, Avtom. Telemekh., 1964, vol. 25, no. 9, pp. 1129-1134.
24. Willems, J.C., Dissipative Dynamical Systems, Part I: General Theory, Arch. Rational Mech. Anal., 1972, vol. 45, pp. 321-351.
25. Yakubovich, V.A., Periodic and Almost Periodic Limiting Modes of the Controllable Systems with Several Nonlinearities, Dokl. Akad. Nauk SSSR, 1966, vol. 171, no. 3, pp. 533-536.
26. Translated into Enaglish as: Periodic and Almost-periodic Limit Modes of Controlled Systems with Several, in General Discontinuous, Nonlinearities, Soviet Math. Dokl. 1966, vol. 7, no. 6, pp. 1517-1521.
27. Fradkov, A.L., Passification of Nonsquare Linear Systems and Yakubovich-Kalman-Popov Lemma, Eur. J. Control, 2003, no. 6, pp. 573-582.
28. Gu, G., Stabilizability Conditions of Multivariable Uncertain Systems via Output Feedback Control, IEEE Trans Automat. Control, 1990, vol. 35, no. 8, pp. 925-927.
29. Abdallah, C., Dorato, P., and Karni, S., SPR Design Using Feedback, in Proc. Am. Control Conf., 1990, pp. 1742, 1743.
30. Weiss, H., Wang, Q., and Speyer, J.L., System Characterization of Positive Real Conditions IEEE Trans. Automat. Control, 1994, vol. 39, no. 3, pp. 540-544.
31. Huang, C.H., Ioannou, P.I., Maroulas, J., and Safonov, M.G., Design of Strictly Positive Real Systems Using Constant Output Feedback, IEEE Trans. Automat. Control, 1999, vol. 44, no. 3, pp. 569-573.
32. Efimov, D.V. and Fradkov, A.L., Adaptive Tuning to Bifurcation for Time-varying Nonlinear Systems, Automatica, 2006, vol. 42(3), pp. 417-425.
33. Bobtsov, A.A. and Nikolaev, N.A., Fradkov Theorem-based Design of the Control of Nonlinear Systems with Functional and Parametric Uncertainties, Avtom. Telemekh., 2005, no. 1, pp. 118-129.
34. Saberi, A., Kokotović, P., and Sussmann, H., Global Stabilization of Partially Linear Composite Systems, SIAM J. Control Optim., 1990, vol. 28, pp. 1491-1503.
35. Bondarko, V.A., Likhtarnikov, A.L., and Fradkov, A.L., Design of Adaptive System of Stabilization of a Distributed-parameter Linear Plant, Avtom. Telemekh., 1979, no. 12, pp. 95-103.
36. Bondarko, V.A. and Fradkov, A.L., Necessary and Sufficient Conditions for Passifiability of the Distributed Linear Systems, Avtom. Telemekh., 2003, no. 4, pp. 3-17.
37. Byrnes, C.I., Isidori, A., and Willems, J.C., Passivity, Feedback Equivalence and the Global Stabilization of Minimum Phase Nonlinear Systems, IEEE Trans. Automat. Control, 1991, vol. AC-36, pp. 1228-1240.
38. Fradkov, A.L. and Hill, D.J., Exponential Feedback Passivity and Stabilizability of Nonlinear Systems, Automatica, 1998, no. 6, pp. 697-703.
39. Zemlyakov, S.D. and Rutkovskii, V.Yu., Design of Algorithms to Modify the Rearrangeable Coefficients in the Self-adjusting Systems with Reference Model, Dokl. Akad. Nauk SSSR, 1967, vol. 174, no. 1, pp. 47-49.
40. Landau, J.D., Adaptive Control Systems. The Model Reference Approach, New York: Dekker, 1979.
41. Petrov, B.N., Rutkovskii, V.Yu., and Zemlyakov, S.D., Adaptivnoe koordinatno-parametricheskoe upravlenie (Adaptive Coordinate-Parametric Control), Moscow: Nauka, 1980.
42. Tsykunov, A.M., Adaptivnoe upravlenie ob"ektami s posledeistviem (Adaptive Control of Delay Plants), Moscow: Nauka, 1984.
43. Popov, A.M. and Fradkov, A.L., Adaptive Control of Singularly Perturbed Plants, in Tr. XI Vses. sov. po probl. upravleniya (Proc. XI All-Union Conf. Control), Erevan, 1983.
44. Ioannou, P.A. and Kokotović, P.V., Adaptive Systems with Reduced Models, Berlin: Springer, 1983.
45. Fradkov, A.L., Design of Adaptive Control System for Nonlinear Singularly Perturbed Plants, Avtom. Telemekh., 1987, no. 6, pp. 100-110.
46. Ilchmann, A., Non-identifier-based Adaptive Control of Dynamical Systems: A Survey, IMA J. Math. Control Info, 1991, no. 8, pp. 321-366.
47. Byrnes, C.I. and Willems, J.C., Adaptive Stabilization of Multivariable Linear Systems, in Proc. 23rd IEEE Conf. Decision and Control, Las Vegas, Nevada, 1984, pp. 1574-1577.
48. Fradkov, A.L., Scheme of the Speed Gradient and its Application to the Problems of Adaptive Control, Avtom. Telemekh., 1979, vol. 40, no. 9, pp. 1333-1342.
49. Derevitskii, D.P. and Fradkov, A.L., Prikladnaya teoriya diskretnykh adaptivnykh sistem upravleniya (Applied Theory of Discrete Adaptive Control Systems), Moscow: Nauka, 1981.
50. Andrievskii, B.R., Using the Method of Matrix Inequalities to Design the Adaptive Tracking Systems, in Optimal'nye i adaptivnye sistemy (Optimal and Adaptive Systems), Frunze: Frunz. Politekh. Inst., 1979, pp. 20-25.
51. Utkin, V.I., Skol'zyashchie rezhimy v zadachakh optimizatsii i upravleniya, Moscow: Nauka, 1981.
52. Utkin, V.I., Skol'zyashchie rezhimy v zadachakh optimizatsii i upravleniya, Moscow: Nauka, 1981. Translated into English under the title Sliding Modes in Control Optimization, Heidelberg: Springer, 1992.
53. Stotsky, A.A., Combined Adaptive and Variable Structure Control, in Variable Structure and Lyapunov Control, Zinober, A.S.I., Ed., London: Springer, 1994, pp. 313-333.
54. Druzhinina, M.V., Nikiforov, V.O., and Fradkov, A.L., Methods of Adaptive Control of Nonlinear Plants by Output, Avtom. Telemekh., 1996, no. 2, pp. 3-33.
55. Nikiforov, V.O. and Fradkov, A.L., Schemes of Adaptive Control with Extended Error. Review, Avtom. Telemekh., 1994, no. 9, pp. 3-26.
56. Fradkov, A.L., Adaptive Stabilization of the Minimum Phase Plants with Vector Input without Measuring the Output Derivatives, Dokl. Ross. Akad. Nauk, 1994, vol. 337, no. 5, pp. 592-594.
57. Translated into English in Physics-Doklady, 1994, vol. 39, no. 8, pp. 550-552.
58. Andrievsky, B.R., Fradkov, A.L., and Stotsky, A.A., Shunt Compensation for Indirect Sliding-mode Adaptive Control, in Proc. 13th IFAC World Congress, San Francisco, 1996, vol. K, pp. 193-198.
59. Andrievskii, B.R. and Fradkov, A.L., Method of Shunting in the Problem of Adaptive Control of the Unstable and Nonminimum Phase Plants, in Mezhdunar. konf. po probl. upravleniya, posv. 60-letiyu IPU RAN. Tez. dokl. (Int. Conf. Control Problems, Abstracts of Papers), Moscow, 1999, vol. 1, pp. 153, 154.
60. Andrievsky, B.R. and Fradkov, A.L., Combined Adaptive Autopilot for an UAV Flight Control, in Proc. IEEE Conf. Control Appl., Glasgow, Sept. 2002, pp. 290, 291.
61. Andrievsky, B.R. and Fradkov, A.L., Combined Adaptive Flight Control System, in Proc. 5th Int. ESA Conf. Spacecraft Guidance, Navigation Control Syst., Frascati, Italy, 2002, ESA-516, Feb. 2003, pp. 299-302.
62. Andrievsky, B.R. and Fradkov, A.L., UAV Guidance System with Combined Adaptive Autopilot, in Proc. IASTED Int. Conf. "Intelligent Systems and Control" (ISC 2003), Salzburg: ACTA Press, 2003, pp. 91-93.
63. Fradkov, A.L. and Andrievskii, B.R., Shunting-based Design of Robust Autopilot, in XI Sankt-Peterb. mezhdunar. konf. po integrirovannym navigatsionnym sistemam (XI St. Petersburg Int. Conf. Integrated Navigation Systems), St. Petersburg: TSNII "Elektropribor, " 2004, pp. 36-38.
64. Fradkov, A.L. and Andrievsky, B.R., Shunting Method for Control of Homing Missiles with Uncertain Parameters, Preprint 16th IFAC Symp. on Automatic Control in Aerospace (ACA'2004), St. Petersburg, 2004, vol. 2, pp. 33-38.
65. Fradkov, A.L. and Andrievsky, B.R., Combined Adaptive Controller for UAV Guidance, Eur. J. Control, 2005, vol. 11, no. 1, pp. 71-79.
66. Apkarian, J., Internet Control, Circuit Cellar, 1999, vol. 110. The manuscript available on the site http://www.circuitcellar.com.
67. Quanser Co., URL: http://www.quanser.com/choice.asp.
68. Laboratoire d'analyse et architechture des systèmes LAAS-CNRS, Toulouse, France, URL: http://www.laas.fr.
69. Andrievskii, B.R., Arzel'e, D., Fradkov, A.L., and Peaucelle, D., Adaptive Control of Pitch Angle for LAAS 'Helicopter Benchmark, ' Proc. 12th St. Petersburg Int. Conf. 'Integrated Navigation Systems, ' May 23-25, 2005, St. Petersburg: CNRI "Elektropribor, " 2005.
70. Andrievsky, B., Fradkov, A., and Peaucelle, D., Adaptive Control Experiments for LAAS "Helicopter" Benchmark, in Proc. 2nd Int. IEEE Conf. "Physics and Control, " St. Petersburg, 2005, pp. 760-766.
71. Fradkov, A.L. and Druzhinina, M.V., Output-feedback Nonlinear Adaptive Control with Implicit Reference Model, in Proc. Am. Control Conf., 2001, pp. 3115, 3116.
72. Blekhman, I.I., Sinkhronizatsiya dinamicheskikh sistem (Synchronization of Dynamic Systems), Moscow: Nauka, 1971.
73. Blekhman, I.I., Vibratsionnaya mekhanika (Vibration Mechanics), Moscow: Nauka, 1994.
74. Pikovskii, A.B., Rozenblyum, M.B., and Kurths, Yu., Sinkhronizatsiya. Fundamental'noe nelineinoe yavlenie (Synchronization. Fundamental Nonlinear Phenomenon), Moscow: Tekhnosfera, 2003.
75. Leonov, G.A. and Smirnova, V.B., Matematicheskie problemy teorii fazovoi sinkhronizatsii (Mathematical Issues of the Phase Synchronization Theory), St. Petersburg: Nauka, 2000.
76. Lindsey, W., Synchronization Systems in Communications and Control, Englewood Cliffs: Prentice Hall, 1972.
77. Translated under the title Sistemy sinkhronizatsii v svyazi i upravlenii, Moscow: Mir, 1978.
78. Fradkov, A.L. and Pogromsky, A.Yu., Introduction to Control of Oscillations and Chaos, Singapore: World Scientific, 1998.
79. Pecora, L.M. and Carroll, T.L., Synchronization in Chaotic Systems, Phys. Rev. Lett., 1990, vol. 64, pp. 821-823.
80. Dmitriev, A.S., Panas, A.I., and Starkov, S.O., Dynamic Chasos as the Paradigm of the Modern Communication Systems, Zarub. Radioelektron., 1997, no. 10, pp. 4-26.
81. IEEE Trans. Circ. Syst., 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.
82. International Journal Circuit Theory Applications. Special issue: Communications, Information Processing and Control Using Chaos, Hasler, M. and Vandewalle, J., Eds., 1999, vol. 27, no. 6.
83. Belykh, V.N., Belykh, I.V., and Hasler, M., Hierarchy and Stability of Partially Synchronous Oscillations of Diffusively Coupled Dynamical Systems, Phys. Rev. E, 2000, vol. 62, no. 5, pp. 6332-6345.
84. Rabinovich, M.I., Abarbanel, H.D.I., Huerta, R., et al., Self-regularization of Chaos in Neural Systems: Experimental and Theoretical Results, IEEE Trans. Circ. Syst. I, 1997, vol. 44, pp. 997-1005.
85. Fradkov, A.L., Nonlinear Adaptive Control: Regulation, Tracking, Oscillations, in Proc. 1st IFAC Workshop "New Trends in Design of Control Systems, " Smolenice, 1994, pp. 426-431.
86. Fradkov, A.L. and Markov, A.Yu., Adaptive Synchronization of Chaotic Systems Based on Speed Gradient Method and Passification, IEEE Trans. Circ. Syst. I, 1997, no. 10, pp. 905-912.
87. Yuan, J. and Wonham, W., Probing Signals for Model Reference Identification, IEEE Trans. Automat. Control, 1977, vol. AC-22, pp. 530-538.
88. Andrievskii, B.R. and Fradkov, A.L., Elementy matematicheskogo modelirovaniya v programmnykh sredakh MATLAB 5 and Scilab (uch. posobie) (Elements of Mathematical Modeling in the MATLAB 5 and Scilab Programming Environments (Tutorial)), St. Petersburg: Nauka, 2001.
89. Fradkov, A.L., Nikiforov, V.O., and Andrievsky, B.R., Adaptive Observers for Nonlinear Nonpassifiable Systems with Application to Signal Transmission, in Proc. 41th IEEE Conf. Dec. Control, Las Vegas, 2002, pp. 4706-4711.
90. Van Trees, H.L., Detection, Estimation, and Modulation Theory. Part II. Theory of Nonlinear Modulation, New York: Wiley, 1971.
91. Translated under the title Teoriya obnaruzheniya, otsenok i modulyatsii. T. 2. Teoriya nelineinoi modulyatsii, Moscow: Sovetskoe Radio, 1975.
92. Fradkov, A.L., Nijmeijer, H., and Markov, A., Adaptive Observer-based Synchronization for Communications, Int. J. Bifurcat. Chaos, 2000, vol. 10(12), pp. 2807-2814.
93. Andrievsky, B.R., Adaptive Synchronization Methods for Signal Transmission on Chaotic Carriers, Math. Comput. Simulation, 2002, vol. 58, nos. 4-6, pp. 285-293.
94. Peaucelle, D., Fradkov, A., and Andrievsky, B., Robust Passification via Static Output Feedback, -LMI Results, in Preprint 16th IFAC World Congress Automat. Control, Prague, 2005.
95. Peaucelle, D., Fradkov A., Andrievsky, B., Passification-based Adaptive Control: Robustness Issues, in Preprint 5th IFAC Symp. Robust Control Design (ROCOND'06), Toulouse, France, July 5-7, 2006.
96. Sun, W., Khargonekar, P., and Shim, D., Solution to the Positive Real Control Problem for Linear Time-invariant Systems, IEEE Trans. Automat. Control, 1994, vol. 39, no. 10, pp. 2034-2046.
97. Fradkov, A.L., Andrievsky, B., and Evans, R.J., Adaptive Observer-based Synchronisation of Chaotic Systems in Presence of Information Constraints, in Preprint 1st IFAC Conf. Anal. Control Chaotic Syst. "Chaos 06, " Rheims, France, 2006.