Abstract
Consideration was given to the class of degenerate problems of designing controller for a multidimensional discrete-time linear plant under stationary perturbations. An algorithm to design an iteratively structured controller providing the desired control performance in the steady-state conditions was proposed.
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REFERENCES
Kwakernaak, H. and Sivan, R., Linear Optimal Control Systems, New York: Wiley, 1972. Translated under the title Lineinye optimal'nye sistemy upravleniya, Moscow: Mir, 1977.
Fomin, V.N., Metody upravleniya lineinymi diskretnymi ob”ektami (Methods of Control of Discrete Linear Plants), Leningrad: Leningrad. Gos. Univ., 1985.
Kolosov, G.E., Sintez optimal'nykh stokhasticheskikh sistem pri sluchainykh vozmushcheniyakh (Design of Optimal Stochastic Systems under Random Perturbations), Moscow: Nauka, 1984.
Kazarinov, Yu.F. and Fomin, V.N., Linear-quadratic Problem of Stochastic Control. III. Nonlinear Optimal Controllers, Avtom. Telemekh., 1993, no. 5, pp. 94–99.
Shchipanov G.V. i teoriya invariantnosti (Shchipanov G.V. and the Invariance Theory), Moscow: Fizmatlit, 2004.
Perov, A.I., Discrete Matrix Lur'e Equation (Singular Case), Avtom. Telemekh., 2003, no. 3, pp. 46–57.
Bunich, A.L., A Method of Successive Improvement in the Design of the Controller of a Linear Discrete Plant, Avtom. Telemekh., 2004, no. 4, pp. 48–55.
Rozanov, Yu.M., Statsionarnye sluchainye protsessy (Stationary Random Processes), Moscow: Nauka, 1990.
Kulebakin, V.S., Theory of Invariance of the Automatically Regulated and Controlled Systems, Proc. I IFAC Cong. on Automatic Control, Moscow: Akad. Nauk SSSR, 1960, vol. 1, pp. 247–255.
Tsypkin, Ya.Z., Moving Approximation and the Principle of Absorption, Dokl. Ross. Akad. Nauk, 1997, vol. 357, no.6, pp. 750–752.
Hannan, E.J., Multiple Time Series, New York: Wiley, 1970. Translated under the title Mnogomernye vremennye ryady, Moscow: Mir, 1974.
Box, G.E.P. and Jenkins, G.M., Time Series Analysis—Forecasting and Control, San Francisco: Holden-Day, 1970. Translated under the title Analiz vremennykh ryadov. Prognoz i upravlenie, Moscow: Mir, 1974.
Lii, K.H. and Rosenblatt, M., Estimation and Deconvolution when the Transfer Function Has Zeros, J. Theor. Probab., 1988, vol. 1, no.1, pp. 93–113.
Olevskii, A.M., Representation of Functions by the Exponents with Positive Frequencies, Usp. Mat. Nauk, 2004, vol. 59, no.1 (355), pp. 169–178.
Rabinovich, M.I. and Trubetskov, D.I., Vvedenie v teoriyu kolebanii i voln (Introduction to the Theory of Oscillations and Waves), Moscow: Nauka, 1984.
Fomin, V.N., Fradkov, A.L., and Yakubovich, V.A., Adaptivnoe upravlenie dinamicheskimi ob”ektami (Adaptive Control of Dynamic Plants), Moscow: Nauka, 1981.
Youla, D.C., Jabr, H., and Bongiorno, J.J., Modern Wiener-Hopf Design of Optimal Controllers. II. The Multivariable Case, IEEE Trans. Automat. Control, 1976, vol. AC-34, no.3, pp. 319–338.
Hormander, L., An Introduction to Complex Analysis in Several Variables, Princeton: van Nostrand, 1966. Translated under the title Vvedenie v teoriyu funktsii neskol'kikh kompleksnykh peremennykh, Moscow: Mir, 1968.
Keel, L. and Bhattacharyya, S.P., Robust, Fragile or Optimal? IEEE Trans. Automat. Control, 1997, vol. 42, no.6, pp. 1098–1105.
Krasovskii, A.A., Historical Overview and State-of-the-Art of the Fundamental Applied Control Science with an Example of Self-organizing Controllers, in Plenary Papers of Int. Conf. Control Problems, Moscow: Inst. Probl. Upravlen., 1999, pp. 4–23.
Teoriya avtomaticheskogo regulirovaniya (Automatic Control Theory), Shatalov, A.S., Ed., Moscow: Vysshaya Shkola, 1977.
Emel'yanov, S.V. and Korovin, S.K., Novye tipy obratnoi svyazi (New Types of Feedbacks), Moscow: Nauka, 1997.
Zames, G., Feedback and Optimal Sensivity: Model Reference Transformation, Multiplicative Seminorms and Approximate Inverses, IEEE Trans. Automat. Control, 1981, vol. AC-26, no.2, pp. 301–320.
Marin, C., Metody Przestazeni Hilberta, Warsaw: PWN, 1959. Translated under the title Metody gil'bertova prostranstva, Moscow: Mir, 1965.
Nikol'skii, N.K., Lektsii ob operatore sdviga (Lectures on Shift Operator), Moscow: Nauka, 1980.
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Translated from Avtomatika i Telemekhanika, No. 11, 2005, pp. 35–45.
Original Russian Text Copyright © 2005 by Bunich.
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Bunich, A.L. Degenerate Problems of Designing the Control System of a Linear Discrete Plant. Autom Remote Control 66, 1733–1742 (2005). https://doi.org/10.1007/s10513-005-0208-9
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DOI: https://doi.org/10.1007/s10513-005-0208-9