Open AccessOn guarantee optimization in control problem with finite set of disturbances
Author(s) -
Mikhail Gomoyunov,
D.A. Serkov
Publication year - 2021
Publication title -
vestnik udmurtskogo universiteta. matematika, mehanika, kompʹûternye nauki
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 8
eISSN - 2076-5959
pISSN - 1994-9197
DOI - 10.35634/vm210406
Subject(s) - piecewise , class (philosophy) , constraint (computer aided design) , mathematical optimization , set (abstract data type) , property (philosophy) , computer science , connection (principal bundle) , key (lock) , control (management) , control theory (sociology) , optimization problem , disturbance (geology) , mathematics , artificial intelligence , mathematical analysis , philosophy , paleontology , geometry , computer security , epistemology , biology , programming language
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.