Decentralized optimal control of dynamical systems under uncertainty
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 7, pp. 1209-1227 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of optimal control of a group of interconnected dynamical objects under uncertainty is considered. The cases are examined in which the centralized control of the group of objects is impossible due to delay in the channel for information exchange between the group members. Optimal self-control algorithms in real time for each dynamical object are proposed. Various types of a priori and current information about the behavior of the group members and about uncertainties in the system are examined. The proposed methods supplement the earlier developed optimal control methods for an individual dynamical system and the methods of decentralized optimal control of deterministic objects. The results are illustrated with examples.
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R. Gabasov; N. M. Dmitruk; F. M. Kirillova. Decentralized optimal control of dynamical systems under uncertainty. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 7, pp. 1209-1227. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a3/

[1] Balashevich N. V., Gabasov R., Kirillova F. M., “Chislennye metody programmnoi i pozitsionnoi optimizatsii lineinykh sistem upravleniya”, Zh. vychisl. matem. i matem. fiz., 40:6 (2000), 838–859 | MR | Zbl

[2] Gabasov R., Dmitruk N. M., Kirillova F. M., “Optimalnoe garantirovannoe upravlenie sistemami s zapazdyvaniem”, Tr. In-ta matem. i mekhan. UrO RAN, 12, no. 2, Ekaterinburg, 2006, 27–47

[3] Kalyaev I. A., Gaiduk A. R., Kapustyan S. G., Raspredelennye sistemy planirovaniya deistvii kollektivov robotov, Yanus-K, M., 2002

[4] Siljak D. D., Decentralized control of complex systems, Acad. Press, New York, 1991 | MR

[5] “Scattolini R. Architectures for distributed and hierarchical model predictive control – A review”, J. Proc. Control, 19 (2009), 723–731 | DOI

[6] Hermans R. M., Lazar M., Jokic A., van den Bosch P. P. J., Proc. 15th IEEE Mediterranean Electrotechn. Conf. (Valletta, Malta, 2010)

[7] Venkat A. N., Hiskens I. A., Rawlings J. B., Wright S. J., “Distributed MPC strategies with application to power system automatic generation control”, IEEE Trans. Control Systems Technol., 16:6 (2008), 1192–1206 | DOI

[8] Gabasov R., Dmitruk N. M., Kirillova F. M., “Optimalnoe detsentralizovannoe upravlenie gruppoi dinamicheskikh ob'ektov”, Zh. vychisl. matem. i matem. fiz., 48:4 (2008), 58–74 | MR

[9] Gabasov R., Dmitruk N. M., Kirillova F. M., “Optimalnoe upravlenie mnogomernymi sistemami po netochnym izmereniyam ikh vykhodnykh signalov”, Tr. In-ta matem. i mekhan. UrO RAN, 10, no. 2, Ekaterinburg, 2004, 33–57 | MR

[10] Gabasov R., Dmitruk N. M., Kirillova F. M., “Optimalnoe nablyudenie pri postoyanno deistvuyuschikh vozmuscheniyakh”, Tr. In-ta matem. i mekhan. UrO RAN, 15, no. 4, Ekaterinburg, 2009, 52–68 | MR

[11] Gabasov R., Kirillova F. M., Dmitruk N. M., “Optimizatsiya mnogomernykh sistem upravleniya s parallelepipednymi ogranicheniyami”, Avtomatika i telemekhan., 2002, no. 3, 3–26 | MR | Zbl

[12] Balashevich N. V., Gabasov R., Kalinin A. I., Kirillova F.M., “Optimalnoe upravlenie nelineinymi sistemami”, Zh. vychisl. matem. i matem. fiz., 42:7 (2002), 969–995 | MR | Zbl

[13] Balashevich N. V., Gabasov R., Kirillova F. M., “Postroenie optimalnykh obratnykh svyazei po matematicheskim modelyam s neopredelennostyu”, Zh. vychisl. matem. i matem. fiz., 44:2 (2004), 265–286 | MR | Zbl

[14] Gabasov R., Kirillova F. M., “Optimal on-line control with delays”, Mem. Different. Equat. and Math. Phys., 31:3 (2004), 35–52 | MR | Zbl