Abstract
Applicability of the block approach to the problem of observation of nonlinear systems in the presence of uncontrollable external perturbations was demonstrated. A block-observable form of the general nonlinear systems was obtained with regard for perturbations. It underlies two types of cascaded procedures for designing the state observers in the class of systems with separable motions: (i) with discontinuous controls and (ii) with high-gain feedbacks. The first procedure relies on the method of equivalent control to restore in a finite time the nonmeasurable components of the state vector and also perturbations. The second procedure estimates the nonmeasurable components of the state vector in the prelimit situation with a given accuracy and retention of the decomposition of the design procedure.
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REFERENCES
Sovremennaya prikladnaya teoriya upravleniya: sinergeticheskii podkhod v teorii upravleniya. II (Applied Modern Control Theory: A Synergistic Approach in the Control Theory, Part II), Kolesnikov, A.A., Ed., Taganrog: Taganrog. Radio-Tekhn. Univ., 2000.
Nikiforov, V.O., Adaptive Nonlinear Tracking with Complete Compensation of Unknown Disturbances, Eur. J. Control, 1998, vol. 4, no.2, pp. 132-139.
Drakunov, S.V., Izosimov, D.B., Luk'yanov, A.G. et al., Principle of Block Control, Avtom. Telemekh., 1990, no. 5, pp. 3-13; no. 6, pp. 20-31.
Utkin, V.I., Method of Motion Separation for Constructing the State Identifier, in Problemy upravleniya mnogosvyaznymi sistemami (Problems of Control of Multivariable Systems), Moscow: Nauka, 1983.
Utkin, V.A., Method of Motion Separation in the Observation Problems, Avtom. Telemekh., 1990, no. 3, pp. 27-37.
Krasnova, S.A., Utkin, V.A., and Mikheev Yu.V., Cascaded Design of the State Observers for Nonlinear Multivariable Systems, Avtom. Telemekh., 2001, no. 2, pp. 43-63.
Stotsky, A., Egardt, B., and Eriksson, S., Variable Structure Control of Engine Idle Speed with Estimation of Unmeasurable Disturbances, J. Dynamic Syst. Measur. Control, 2000, vol. 122, no.4, pp. 599-603.
Krasnova, S.A., Cascaded Design of the Manipulator Control System Taking into Account Dynamics of Electric Drives, Avtom. Telemekh., 2001, no. 11, pp. 51-72.
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.
Isidori, A., Nonlinear Control System, New York: Springer, 1995.
Utkin, V.I., Skol'zyashchie rezhimy v zadachakh optimizatsii i upravleniya, Moscow: Nauka, 1987. Translated under the title Sliding Modes in Optimization and Control, Heidelberg: Springer, 1992.
Luk'yanov, A.G. and Utkin, V.I., Methods of Reducing Dynamic Systems to the Regular Form, Avtom. Telemekh., 1981, no. 4, pp. 5-13.
Luk'yanov, A.G., Block Method of Designing Nonlinear Systems in Sliding Modes, Avtom. Telemekh., 1998, no. 7, pp. 14-34.
Rashevskii, P.K., Geometricheskaya teoriya uravnenii s chastnymi proizvodnymi (Geometric Theory of Partial Differential Equations), Moscow: Gostekhizdat, 1947.
Krasnova, S.A., Decomposition State Observer Design for Nonlinear Systems, in “NOLCOS'01”, St. Petersburg, 2001, vol. 4, pp. 997-1002.
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Krasnova, S.A. Cascaded Design of the State Observer for Nonlinear Systems in the Presence of External Perturbations. Automation and Remote Control 64, 1–22 (2003). https://doi.org/10.1023/A:1021894106897
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DOI: https://doi.org/10.1023/A:1021894106897