Informatics and Applications
2021, Volume 15, Issue 1, pp 11-17
ON SOME SPECIAL CASES IN THE PROBLEM OF STOCHASTIC DIFFERENTIAL SYSTEM OUTPUT CONTROL BY THE QUADRATIC CRITERION
Abstract
A general study of the optimal control problem for the Ito diffusion process and linear controlled output with the quadratic quality criterion was carried out in the author's previous works (coauthored by A. I. Stefanovich).
An analysis of the available results allows to single out some models that are of a particular nature in relation to the general setting but have special practical significance. This article examines two such particular models. The first model is determined by the assumption of linear drift in the equation of state while maintaining nonlinear diffusion. It is shown that such a model provides linearity to the optimal control and the absence of the need to solve a parabolic equation for its implementation. But in this case, the quadratic Bellman function does not appear in the problem, the corresponding expression, as in the general case, is described by the solution of a parabolic equation and retains a meaningful stochastic interpretation expressed by the Feynman-Katz formula. The second model implements the assumption about the dependence of disturbances in the equations of state and output. The modified dynamic programming equation is solved in the same way as in the general case considered in previous works, including and within the framework of a combined model involving both cases presented. This model will be especially useful in the problems with incomplete information, when the assumption of the presence of complete information about the state and output will be replaced by a description of the observation system, in which the output is interpreted as indirect observations of the state. A numerical example, studied in detail in the author's previous works (coauthored by A. I. Stefanovich), is briefly discussed, since it turns out that it satisfies the assumption of linear drift in the equation of state and, accordingly, the previously obtained approximate solutions can be refined.
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[+] About this article
Title
ON SOME SPECIAL CASES IN THE PROBLEM OF STOCHASTIC DIFFERENTIAL SYSTEM OUTPUT CONTROL BY THE QUADRATIC CRITERION
Journal
Informatics and Applications
2021, Volume 15, Issue 1, pp 11-17
Cover Date
2021-03-30
DOI
10.14357/19922264210102
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
stochastic differential equation; optimal control; system output control; stochastic differential systems with multiplicative and dependent disturbances
Authors
A. V. Bosov 
Author Affiliations
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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