Abstract
A method of decomposition analysis and design is developed for estimating the unmeasurable components of the state vector and external perturbations of a wide class by the methods of design of systems with discontinuous controls in the correction circuit of the dynamic observer. It is helpful in identifying the observable subspace of maximal dimension of the state vector and observable combinations of the components of the state vector, and in solving the estimation problem in a finite time without the need for joint analysis and design of a closed system with an observer.
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REFERENCES
Utkin, V.I., Skol'zyashchie rezhimy v zadachakh upravleniya i optimizatsii (Sliding Modes in Control and Optimization Problems), Moscow: Nauka, 1981.
Meerov, M.V., Sistemy mnogosvyaznogo regulirovaniya (Multiconnected Control Systems), Moscow: Nauka, 1965.
Utkin, V.A. and Utkin, V.I., The Method of Separation in Invariance Problems, Avtom. Telemekh., 1983, no. 12, pp. 39–48.
Sovremennaya prikladnaya teoriya upravleniya: sinergeticheskii podkhod v teorii upravleniya (Modern Applied Control Theory: A Synergetic Approach to Control Theory), Kolesnikov, A.A., Ed., Taganrog: TRTU, 2000.
Miroshnik, I.V., Nikiforov, V.A., and Fradkov, A.L., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (A Nonlinear Adaptive Control for Complex Dynamic Systems), St. Petersburg: Nauka, 2000.
Utkin, V.A., Invariance and Self-Sufficiency in Systems with Separated Motions, Avtom. Telemekh., 2001, no. 11, pp. 73–94.
Shabanovich, A., Automatic Amplitude Tuner for the Discontinuities in Control of Variable-Structure Systems, in Novye napravleniya v teorii sistem s peremennoi strukturoi (SPS) (New Trends in the Theory of Variable-Structure Systems), Moscow: VNIISI, 1980, vol. 4, pp. 73–77.
Ciccarella, G., Dalla Mora, M., and German, A., A Luenberger-like Observer for Nonlinear Systems, Int. J. Control, 1993, vol. 57, no.3, pp. 537–556.
Krasnova, S.A., Cascade Design of State Observer for Nonlinear Systems under External Perturbations, Avtom. Telemekh., 2003, no. 1, pp. 31–54.
Isidori, A., Nonlinear Control Systems, New York: Springer-Verlag, 1989.
Krasnova, S.A., Utkin, V.A., and Mikheev, Yu.V., Cascade Design of State Observers for Nonlinear Multidimensional Systems, Avtom. Telemekh., 2001, no. 2, pp. 43–63.
Utkin, V.A., The Method of Separation in Problems of Observation, Avtom. Telemekh., 1990, no. 3, pp. 27–37.
Petrov, B.N., Rutkovskii, V.Yu., and Zemlyakov, S.D., Adaptivnoe koordinatno-parametricheskoe upravlenie nestatsionarnymi ob"ektami (Adaptive Coordinate-Parametric Control of Time-Varying Systems), Moscow: Nauka, 1980.
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Translated from Avtomatika i Telemekhanika, No. 10, 2005, pp. 54–69.
Original Russian Text Copyright © 2005 by Krasnova, Kuznetsov.
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Krasnova, S.A., Kuznetsov, S.I. Uncontrollable Perturbations of Nonlinear Dynamic Systems: Estimation on Moving Modes. Autom Remote Control 66, 1580–1593 (2005). https://doi.org/10.1007/s10513-005-0192-0
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DOI: https://doi.org/10.1007/s10513-005-0192-0