Geodesic
Motion correction of a statistically uncertain system under communication constraints
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 4, pp. 20-31
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The problem of motion correction of a controlled system is considered. It is required to minimize a terminal functional under statistical uncertainty of the disturbance and incomplete information about the state of the system. Reachable sets of filtering and prediction equations are used; these sets are uniquely determined for a given time moment by the realizations of the observed signal and the chosen control. A modification of the correction problem under communication constraints is considered, in which the bounded capacity of the digital date transfer channel is taken into account. It is assumed that the object is equipped with a computation facility that can remember the measured information, process it with a high level of accuracy, transmit it, and receive coded signals via communication channels. Signals in the form of words of bounded length consisting of integers come to the control and information processing center (CIPC) at discrete time moments. For simplicity, the communication channel is assumed to be noise- and delay-free. The coding device in the communication channel is used for transmitting information about the measured parameters of the object to the CIPC and the control action from the CIPC to the object. In the CIPC, the information about the parameters is decoded and used for calculating the correction moments and optimal control. Relations between the reconstruction accuracy of the measured parameters and the optimal value of the functional are obtained as well as between the length of the transmitted word and the transmitting frequency. Several results are exemplified.
Mots-clés : motion correction
Keywords: program control, communication channel. 
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B. I. Anan'ev. Motion correction of a statistically uncertain system under communication constraints. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 4, pp. 20-31. http://geodesic.mathdoc.fr/item/TIMM_2009_15_4_a2/

[1] Krasovskii N. N., “Igrovaya zadacha o korrektsii dvizheniya”, Prikl. matematika i mekhanika, 33:3 (1969), 386–396 | MR

[2] Ananev B. I., Kurzhanskii A. B., Shelementev G. S., “Minimaksnyi sintez v zadachakh impulsnogo navedeniya i korrektsii dvizheniya”, Prikl. matematika i mekhanika, 40:1 (1976), 3–13

[3] Kurzhanskii A. B., Upravlenie i nablyudenie v usloviyakh neopredelennosti, Nauka, M., 1977, 392 pp. | MR | Zbl

[4] Chernousko F. L., “Minimaksnaya zadacha odnorazovoi korrektsii pri pogreshnosti izmerenii”, Prikl. matematika i mekhanika, 32:4 (1968), 587–595 | MR

[5] Ananev B. I., “Minimaksnaya kvadratichnaya zadacha korrektsii dvizheniya”, Prikl. matematika i mekhanika, 41:3 (1977), 436–445 | MR

[6] Chernousko F. L., Kolmanovskii V. B., Optimalnoe upravlenie pri sluchainykh vozmuscheniyakh, Nauka, M., 1978, 351 pp. | MR

[7] Ananev B. I., Gredasova N. V., “Mnogokratnaya korrektsiya dvizheniya upravlyaemoi sistemy v usloviyakh neopredelennosti”, Sb. Ural. gos. tekhn. un-ta, UPI, 2005, 1–5 | MR

[8] Liptser R. Sh., Shiryaev A. N., Statistika sluchainykh protsessov, Nauka, M., 1974, 696 pp. | MR | Zbl

[9] Milstein G. N., Tretyakov M. V., Stochastic numerics for mathematical physics, Springer-Verlag, New York, 2004, 596 pp. | MR | Zbl

[10] Ostrëm K., Vvedenie v stokhasticheskuyu teoriyu upravleniya, Mir, M., 1973, 321 pp.

[11] Ananev B. I., Anikin S. A., “Zadacha vosstanovleniya vkhodnykh vozdeistvii pri kommunikatsionnykh ogranicheniyakh”, Avtomatika i telemekhanika, 2009, no. 7, 73–84