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Degenerate linear-quadratic problem of discrete plant under uncertainty. (English. Russian original) Zbl 1269.49065
Autom. Remote Control 72, No. 11, 2351-2363 (2011); translation from Avtom. Telemekh. 2011, No. 11, 143-156 (2011).
Summary: Consideration is given to the linear-quadratic problem for the stationary discrete plants with a prescribed cost of control under incomplete information about the spectral composition of perturbations. An efficiently realizable algorithm to design a controller guaranteeing the given cost of control for the class of perturbations with localization of spectra in the a-priori defined frequency ranges is proposed.

MSC:
49N10 Linear-quadratic optimal control problems
49N30 Problems with incomplete information (optimization)
49M30 Other numerical methods in calculus of variations (MSC2010)
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[1] Letov, A.M., Analytical Controller Design. I–V, Autom. Remote Control, 1960, vol. 21, no. 4, pp. 303–306; no. 5, pp. 389–393; no. 6, pp. 458–461; 1961, vol. 22, no. 4, pp. 363–372; 1962, vol. 23, no. 11, pp. 1319–1327. · Zbl 0182.48203
[2] Kalman, R., Contributions to the Theory of Optimal Control, Boletin de la Sociedad Mat. Mexican. Secunda ser., 1960, no. 1, pp. 102–119. · Zbl 0112.06303
[3] Emel’yanov, S.V. and Korovin, S.K., Novye tipy obratnoi svyazi. Upravlenie pri neopredelennosti (New Types of Feedback. Control under Uncertainty), Moscow: Nauka, 1997.
[4] Tsypkin, Ya.Z., Robust Optimal Discrete Control Systems, Autom. Remote Control, 1999, vol. 60, no. 3, part 1, pp. 315–324. · Zbl 1273.93108
[5] Rozanov, Yu.A., Statsionarnye sluchainye protsessy (Stationary Random Processes), Moscow: Nauka, 1990. · Zbl 0721.60040
[6] Bunich, A.L., Degenerate Problems of Control System Design for Discrete Linear Plants, Probl. Upravlen., 2009, no. 5, pp. 2–8.
[7] Fomin, V.N., Fradkov, A.L., and Yakubovich, V.A., Adaptivnoe upravlenie dinamicheskimi ob”ektami (Adaptive Control of Dynamic Plants), Moscow: Nauka, 1981. · Zbl 0522.93002
[8] Bellman, R. and Kalaba, R., Dynamic Programming and Adaptive Control Processes: Mathematical Foundations, IRE Trans. Automat. Control, 1960, vol. AC-5, pp. 5–10. · doi:10.1109/TAC.1960.6429288
[9] Bellman, R. and Kalaba, R., Dynamic Programming and Modern Control Theory, New York: Academic, 1965. · Zbl 0139.04502
[10] Raibman, N.S. and Chadeev, V.M., Adaptivnye modeli v sistemakh upravleniya (Adaptive Models in the Control Systems), Moscow: Sovetskoe Radio, 1966.
[11] Fel’dbaum, A.A., Osnovy teorii optimal’nykh avtomaticheskikh sistem (Fundamentals of the Theory of Optimal Automatic Systems), Moscow: Nauka, 1966.
[12] Barabanov, A.E. and Pervozvanskii, A.A., Optimization by he Frequency-uniform Criteria (H-theory), Autom. Remote Control, 1992, vol. 53, no. 9, part 1, pp. 1301–1327.
[13] Vladimirov, I.G., Kurdyukov, A.P., and Semenov, A.V., Stochastic Problem of H-optimization, Dokl. Ross. Akad. Nauk, 1995, vol. 343, no. 5, pp. 607–609. · Zbl 0875.93105
[14] Bunich, A.L., Degenerate Problems of Designing the Control System of a Linear Discrete Plant, Autom. Remote Control, 2005, vol. 66, no. 11, pp. 1733–1742. · Zbl 1126.93342 · doi:10.1007/s10513-005-0208-9
[15] Fomin, V.N., Metody upravleniya lineinymi diskretnymi ob”ektami (Methods of Control of Discrete Linear Plants), Leningrad: Leningr. Gos. Univ., 1985. · Zbl 0941.93508
[16] Kazarinov, Yu.F., Nonlinear Optimal Controllers in Stochastic Systems with a Linear Plant and Quadratic Functional, Autom. Remote Control, 1986, vol. 47, no. 1, part 1, pp. 50–57. · Zbl 0603.93070
[17] Piunovskii, A.B., Upravlenie sluchainymi posledovatel’nostyami v zadachakh s ogranicheniyami (Control of Random Sequences in the Problems with Constraints), Moscow: RFFI, 1996.
[18] Shteinberg, Sh.E., Serezhin L.P., et al., Problems of Design and Operation of Effective Control Systems, Promyshl. ASU i Kontrollery, 2004, no. 7, pp. 1–7.
[19] Qin, S.J. and Badgwell, T.A., A Survey of Industrial Control Technology, Contr. Eng. Practice, 2003, vol. 11, no. 7, pp. 733–764. · doi:10.1016/S0967-0661(02)00186-7
[20] Krasovskii, A.A., Historical Overview and State-of-the-Art of the Fundamental Applied Science of Control in Terms of Self-organizing Controllers, in Int. Conf. Control Probl., Plenary Papers, Moscow: Inst. Probl. Upravlen., 1999, pp. 4–23.
[21] Wiener, N., Cybernetics or Control and Communication in the Animals and the Machines, New York: MIT Press, 1961. Translated under the title Kibernetika ili upravlenie i svyaz’ v zhivotnom i mashine, Moscow: Sovetskoe Radio, 1968.
[22] Lundquist, L. and Yakubovich, V.A., Universal Controllers for Optimal Signal Tracking in Discrete Linear Systems, Dokl. Ross. Akad. Nauk, 1998, vol. 361, no. 2, pp. 177–180. · Zbl 0958.93058
[23] Olevskii, A.M., Representation of Functions by Exponents with Positive Frequencies, Usp. Mat. Nauk, 2004, vol. 59, no. 1 (355), pp. 169–178. · doi:10.4213/rm707
[24] Bogatyrev, A.B., Ekstremal’nye mnogochleny i rimanovy poverkhnosti (Extremal Polynomials and Riemann Surfaces), Moscow: MTSNMO, 2005. · Zbl 1243.65001
[25] Kravtsov, Yu.A., Randomness, Determinacy, Predictability, Usp. Fiz. Nauk, 1989, vol. 158, no. 1, pp. 93–122. · doi:10.3367/UFNr.0158.198905c.0093
[26] Pinsker, M.S. and Prelov, V.V., On Faultless Filtration of some Stationary Processes, Usp. Mat. Nauk, 1997, vol. 52, no. 2 (314), pp. 109–118. · doi:10.4213/rm821
[27] Oppenheim, A.V. and Schafer, R.W., Digital Signal Processing, Englewood Cliffs: Prentice Hall, 1989. Translated under the title Tsifrovaya obrabotka signalov, Moscow: Tekhnosfera, 2006. · Zbl 0369.94002
[28] Suetin, P.K., Ryady po mnogochlenam Fabera (Series in Faber Polynomials), Moscow: Nauka, 1984. · Zbl 0936.30026
[29] Rosenblatt, M. and Lii, K.S., Estimation and Deconvolution When the Transfer Function Has Zeros, J. Theor. Prob., 1988, vol. 1, no. 1, pp. 93–113. · Zbl 0668.62071 · doi:10.1007/BF01076289
[30] Babayan, N.M., On Asymptotic Behavior of the Forecast Error in the Singular Case, Teor. Veroyatn. Primen., 1984, vol. XXIX, no. 1, pp. 147–150. · Zbl 0531.60046
[31] Feller, W., An Introduction to Probability Theory and Its Applications, New York: Wiley, 1970, vol. 1, 3rd ed., 1971, vol. 2, 2nd ed. Translated under the title Vvedenie v teoriyu veroyatnostei i ee prilozheniya, Moscow: Mir, 1984, tom 2. · Zbl 0039.13201
[32] Hörmander, K., 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.
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