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Russia Chelyabinsk
Section  Mathematics 
Title  Dynamic control problem under interference with a given set of correction momenta 
Author(s)  Ukhobotov V.I.^{a}, Stabulit I.S.^{a} 
Affiliations  Chelyabinsk State University^{a} 
Abstract  We consider a dynamic control system under interference. A set of correction momenta of the controls is given. The problem of phase point retention in a given collection of sets at correction momenta is considered. Instantaneous change of a position is admissible. Necessary and sufficient conditions for the possibility of retention are found. As an example, we consider a discrete linear control problem under interference and with the onedimensional aim. The condition of onedimensionality of the aim means that the modulus of the value of a given linear function of the phase variables at a fixed moment of the control process end should not be more than a given number. For this problem, necessary and sufficient conditions are found in an explicit form, the fulfillment of which guarantees the existence of an admissible control that ensures the achievement of the aim for any admissible realization of the interference. This control is constructed in an explicit form, and information about the realized value of the interference is not used. We constructed the interference which guarantees that the aim will not be reached at any admissible control from the initial state that does not satisfy the obtained conditions. 
Keywords  control, interference, correction 
UDC  517.977 
MSC  91A23, 49N75 
DOI  10.20537/vm180107 
Received  28 December 2017 
Language  Russian 
Citation  Ukhobotov V.I., Stabulit I.S. Dynamic control problem under interference with a given set of correction momenta, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 1, pp. 7481. 
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