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Cybernetics And Systems Analysis
International Theoretical Science Journal
Volume 56 >>> № 2 MARCH — APRIL 2020
UDC 517.9
L.A. Vlasenko1, A.G. Rutkas2, V.V. Semenets3, A.A. Chikrii4


1 Kharkiv National University of Radio Electronics, Kharkiv, Ukraine

 lara@rutrus.com

2 Kharkiv National University of Radio Electronics, Kharkiv, Ukraine

 anatoly@rutrus.com

3 Kharkiv National University of Radio Electronics, Kharkiv, Ukraine

 valery.semenets@nure.ua

4 V.M. Glushkov Institute of Cybernetics, National Academy
of Sciences of Ukraine, Kyiv, Ukraine

 chik@insyg.kiev.ua

ON THE STOCHASTIC OPTIMAL CONTROL OF A DESCRIPTOR SYSTEM

Abstract. We study the optimal control problem of a descriptor system, whose evolution is described by Ito’s differential-algebraic equation. The quadratic cost functional is considered. The main constraint is that the characteristic matrix pencil corresponding to the equation is regular. We establish the conditions for the existence and uniqueness of the optimal control and the corresponding optimal state. The results are illustrated on an example of a descriptor system that describes transient states in a radio engineering filter with random perturbations in the form of white noise.

Keywords: stochastic differential algebraic equation, Wiener random process, quadratic performance functional, stochastic optimal control, radio engineering filter, transient state.



FULL TEXT

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