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Kucěra, Vladimir; Šebek, Michael

A polynomial solution to regulation and tracking. II: Stochastic problem. (English) Zbl 0554.93075

Kybernetika 20, 257-282 (1984).
[For part I see ibid. 20, 177-188 (1984; Zbl 0542.93013)]. This is a paper dealing with the much studied linear quadratic control problem in both a deterministic and a stochastic version. This reviewer has trouble getting excited no matter how well such familiar results are presented.
Reviewer: J.Rissanen

Cited in 3 Documents

MSC:

93E20 Optimal stochastic control
93C55 Discrete-time control/observation systems
12E12 Equations in general fields
12D05 Polynomials in real and complex fields: factorization

Keywords:

linear quadratic control

Citations:

Zbl 0542.93013
Cite Review PDF
Full Text: EuDML

References:

[1] K. J. Åström: Introduction to Stochastic Control Theory. Academic, New York 1970.
[2] T. Kailath: Linear Systems. Prentice-Hall, Englewood Cliffs 1980. · Zbl 0454.93001
[3] V. Kučera: State space approach to discrete linear control. Kybernetika 8 (1972), 233 - 251.
[4] V. Kučera: Algebraic Theory of Discrete Linear Control. (in Czech). Academia, Praha 1978.
[5] V. Kučera: Discrete Linear Control - The Polynomial Equation Approach. Wiley, Chichester 1979.
[6] V. Kučera: Discrete stochastic regulation and tracking. Kybernetika 76 (1980), 263 - 272.
[7] V. Kučera: Linear quadratic control - State space vs. polynomial equations. Kybernetika 79 (1983), 185-195. · Zbl 0549.93030
[8] V. Peterka: On steady state minimum variance control strategy. Kybernetika 8 (1972), 219-232. · Zbl 0256.93070
[9] V. Peterka: Predictor-based self-tuning control. Automatica 20 (1984), 39 - 50. · Zbl 0539.93054 · doi:10.1016/0005-1098(84)90063-3
[10] M. Šebek: Optimal tracking via polynomial matrix equations. Internat. J. Systems Sci. 12 (1981), 357-369. · Zbl 0458.93040 · doi:10.1080/00207728108963751
[11] M. Šebek: Polynomial design of stochastic tracking systems. IEEE Trans. Automat. Control AC-27 (1982), 468-470. · Zbl 0488.93066 · doi:10.1109/TAC.1982.1102933
[12] M. Šebek, V. Kučera: Polynomial approach to quadratic tracking in discrete linear systems. IEEE Trans. Automat. Control AC-27 (1982), 1248-1250.
[13] L. N. Volgin: The Fundamentals of the Theory of Controlling Machines. (in Russian). Soviet Radio, Moscow 1962.
[14] W. A. Wolovich: Linear Multivariable Systems. Springer-Verlag, New York 1974. · Zbl 0291.93002
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