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This article is cited in 3 scientific papers (total in 3 papers)
Stochastic differential system output control by the quadratic criterion. III. Optimal control properties analysis
A. V. Bosov, A. I. Stefanovich 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
Abstract:
The investigation of the optimal control problem for the Ito diffusion process and linear controlled output with a quadratic quality criterion is continued. The properties of the optimal solution defined by the Bellman function of the form $V_t(y,z)=\alpha_tz^2+\beta_t(y)z+\gamma_t(y)$, whose coefficients $\beta_t(y)$ and $\gamma_t(y)$ are described by linear parabolic equations, are studied. For these coefficients, alternative equivalent descriptions are defined in the form of stochastic differential equations and a theoretical-to-probabilistic representation of their solutions, known as the Kolmogorov equation. It is shown that the obtained differential representation is equivalent to the Feynman–Kac integral formula. In the future, the obtained description of the coefficients and, as a result, the solutions of the original control problem can be used to implement an alternative numerical method for calculating them as a result of computer simulation of the solution of a stochastic differential equation.
Keywords:
stochastic differential equation, optimal control, Bellman function, linear differential equations of parabolic type, Kolmogorov equation, Feynman–Kac formula.
Received: 21.02.2019
Citation:
A. V. Bosov, A. I. Stefanovich, “Stochastic differential system output control by the quadratic criterion. III. Optimal control properties analysis”, Inform. Primen., 13:3 (2019), 41–49
Linking options:
https://www.mathnet.ru/eng/ia608 https://www.mathnet.ru/eng/ia/v13/i3/p41
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Abstract page: | 191 | Full-text PDF : | 43 | References: | 24 |
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