Abstract
Solution of the problem of adaptive control of nonlinear plants with nonconvex-in-control-parameters functions of the right sides of their state equations was presented. Conditions for existence of the auxiliary functions for designing the adaptive control algorithms were formulated. For the adaptive systems using the introduced adaptation algorithms, theorems of attainability of the control goals were proved. The theoretical propositions were supported by computer simulation.
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REFERENCES
Zangwill, W.I., Nonlinear Programming. A Unified Approach, Englewood Cliffs: Prentice Hall, 1969. Translated under the title Nelineinoe programmirovanie. Edinyi podkhod, Moscow: Sovetskoe Radio, 1973.
Fomin, V.N., Fradkov, A.L., and Yakubovich, V.A., Adaptivnoe upravlenie dinamicheskimi ob"ektami (Adaptive Control of Dynamic Plants), Moscow: Nauka, 1981.
Terekhov, V.A. and Tyukin, I.Yu., Adaptive Control on Manifolds, in Proc. 6th St.-Petersburg Symp. Adaptive Systems Theory (SPAS`99), September 7–9, 1999, vol. 1, pp. 254 (in English), vol. 2, pp. 157–160 (in Russian).
Terekhov, V.A. and Tyukin, I.Yu., Adaptive Control on Manifolds of Nonlinear Control Plants with Complex and Oscillation Dynamic, in Proc. 2nd Int. Conf. “Control of Oscillations and Chaos (COC'2000),” St. Petersburg, July 5–7, 2000, vol. 2, pp. 187–189.
Fradkov, A.L., Adaptivnoe upravlenie v slozhnykh sistemakh: bespoiskovye metody (Adaptive Control in Complex Systems: Searchless Methods), Moscow: Nauka, 1990.
Krstič, M., Kanellakopoulos, I., and Kokotovič, P.V., Nonlinear and Adaptive Control Design, NewYork: Wiley, 1995.
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.
Narendra, K.S. and Annaswamy, A.M., Stable Adaptive Systems, Englewood Cliffs: Prentice Hall, 1989.
Ai-Poh Loh, Annaswamy, A.M., and Skantz, F.P., Adaptation in the Presence of a General Nonlinear Parameterization: An Error Model Approach, IEEE Trans. Autom. Control, 1999, vol. 144, no. 9, pp. 1634–1653.
Terekhov, V.A., Efimov, D.V., Tyukin, I.Yu., and Antonov, V.N., Neirosetevye sistemy upravleniya (Neural Network-Based Control Systems) St. Petersburg: S.-Peterburg. Gos. Univ., 1999.
Efimov, D.V., Terekhov, V.A., and Tyukin, I.Yu., An Adaptive Control System with a Neural Network, Izv. GETU: Ser. Sist. Obrabotki Inf. Upravlen., 1996, vol. 490, pp. 32–35.
Terekhov, V.A, Efimov, D.V., and Tyukin, I.Yu., Adaptive Control Systems Based on Multilayer Neural Networks, Izv. GETU, Ser. Met. Apparatno-programn. Sredstva Tsifr. Obrabotki Sign., 1996, vol. 498, pp. 36–56.
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Prokhorov, D.V., Terekhov, V.A. & Tyukin, I.Y. On the Applicability Conditions for the Algorithms of Adaptive Control in Nonconvex Problems. Automation and Remote Control 63, 262–279 (2002). https://doi.org/10.1023/A:1014299608899
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DOI: https://doi.org/10.1023/A:1014299608899