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|Title:||On Guarantee Optimization in Control Problem with Finite Set of Disturbances|
|Other Titles:||Об оптимизации гарантии в задаче управления с конечным множеством помех|
|Authors:||Gomoyunov, M. I.|
Serkov, D. A.
|Publisher:||Udmurt State University|
Udmurt State University
|Citation:||Gomoyunov M. I. On Guarantee Optimization in Control Problem with Finite Set of Disturbances [Об оптимизации гарантии в задаче управления с конечным множеством помех] / M. I. Gomoyunov, D. A. Serkov // Vestnik Udmurtskogo Universiteta: Matematika, Mekhanika, Komp'yuternye Nauki. — 2021. — Vol. 31. — Iss. 4. — P. 613-628.|
|Abstract:||In this paper, we deal with a control problem under conditions of disturbances, which is stated as a problem of optimization of the guaranteed result. Compared to the classical formulation of such problems, we assume that the set of admissible disturbances is finite and consists of piecewise continuous functions. In connection with this additional functional constraint on the disturbance, we introduce an appropriate class of non-anticipative control strategies and consider the corresponding value of the optimal guaranteed result. under a technical assumption concerning a property of distinguishability of the admissible disturbances, we prove that this result can be achieved by using control strategies with full memory. As a consequence, we establish unimprovability of the class of full-memory strategies. A key element of the proof is a procedure of recovering the disturbance acting in the system, which allows us to associate every non-anticipative strategy with a full-memory strategy providing a close guaranteed result. The paper concludes with an illustrative example. © M. I. Gomoyunov, D. A. Serkov.|
|Keywords:||CONTROL PROBLEM under DISTURBANCES|
OPTIMAL GUARANTEED RESULT
RECOVERY OF DISTURBANCES
|metadata.dc.description.sponsorship:||The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075–02–2021–1383).|
|Appears in Collections:||Научные публикации, проиндексированные в SCOPUS и WoS CC|
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