ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

The small parameter method for solving the problem of optimal stabilization of systems with random structure and random jumps of the phase vector


Tatyana Viktorovna Zavyalova

National Research Technological University (MISiS),
Moscow, Leninsky Prospect, 6, bld. 7
cand. phys.-mat. sciences, associate professor


The paper considers a linear-quadratic optimal control problem for a system with a random structure. System parameters are exposed to a purely discontinuous Markov process with given transition probabilities. It is assumed that at a random time, structural state of the system changes and its phase vector changes abruptly. Earlier, the conditions for finding the optimal control in the form of integral matrix equations were obtained by V.Buhalev. But these equations are cumbersome for practical use. In this paper we consider the construction of optimal control using the small parameter method, which allows us to construct tyhe control in the form of a convergent series in powers of a small parameter.



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