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Optimal conditional relative observation of nonstationary linear systems. (Russian, English) Zbl 1108.93025

Prikl. Mat. Mekh. 68, No. 4, 586-601 (2004); translation in J. Appl. Math. Mech. 68, No. 4, 523-536 (2004).
The authors dwell on an optimal observation problem appeared at the control under uncertainty conditions. The problem is studied for three types of noises in measuring device. Construction methods are described for a posteriori and positional solutions. The results are illustrated by an example of the forth order dynamical system observation.

MSC:

93B07 Observability
93C05 Linear systems in control theory
93C41 Control/observation systems with incomplete information
Full Text: DOI

References:

[1] Krasovskii, N. N., The theory of the controllability and observability of linear dynamical systems, Prikl. Mat. Mekh., 28, 1, 3-14 (1964) · Zbl 0135.31402
[2] Schweppe, E. C., Recursive state estimation: unknown but bounded errors and system inputs, IEEE Trans. Automat. Control, AC-13, 1, 22-68 (1968)
[3] Kurzhanskii, A. B., Control and Observation under Conditions of Uncertainty (1977), Nauka: Nauka Warsaw · Zbl 0461.93001
[4] Chernous’ko, F. L., Estimation of the Phase State of Dynamical Systems. The Method of Ellipsoids (1988), Nauka: Nauka Moscow · Zbl 0704.70023
[5] (Leondes, C. T., Control and Dynamic Systems, Vol. 12 (1976), Academic Press: Academic Press Moscow) · Zbl 0324.00029
[6] Gabasov, R.; Kirillova, F. M., Allied problems of control, observation, and identification, Dokl. Akad. Nauk BSSR, 34, 9, 777-780 (1990) · Zbl 0716.93004
[7] Gabasov, R.; Zhevnyak, R. M.; Kirillova, F. M.; Kopeikina, T. B., Relative observability of linear systems, 1. Ordinary systems, Avtomatika i Telemekhanika, 8, 5-15 (1972)
[8] Gabasov, R.; Zhevnyak, R. M.; Kirillova, F. M.; Kopeikina, T. B., Relative observability of linear systems, 2. Observations under permanent disturbances, Avtomatika i Telemekhanika, 10, 5-15 (1972)
[9] Gabasov, R.; Zhevnyak, R. M.; Kirillova, F. M.; Kopeikina, T. B., Conditional observability of linear systems, Problemy Upravleniya i Teorii Informatsii, 1, 3-4, 217-238 (1972) · Zbl 0415.93005
[10] Gabasov, R.; Kirillova, F. M.; Kostyukova, 0. I., Synthesis of optimal controls under conditions of incomplete and inaccurate information about their state, Trudy Mat. Inst. Im. Steklova Ross. Akad. Nauk, 211, 140-152 (1995) · Zbl 0903.49014
[11] Balashevich, N. V.; Gabasov, R.; Kirillova, E. M., Numerical methods of programmed and positional optimization of linear control systems, Zhum. Vychisl Mat. Mat. Fiziki, 40, 6, 838-859 (2000) · Zbl 0990.49023
[12] Gabasov, R.; Kirillova, F. M.; Tyatyushkin, A. I., Constructive Methods of Optimization, Part I, LinearProblems (1984), Izd. Universitetskoye: Izd. Universitetskoye New York · Zbl 0581.90051
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