Informatics and Applications
2020, Volume 14, Issue 1, pp 2430
STOCHASTIC DIFFERENTIAL SYSTEM OUTPUT CONTROL BY THE QUADRATIC CRITERION. IV. ALTERNATIVE NUMERICAL DECISION
 A. V. Bosov
 A. I. Stefanovich
Abstract
In the study of the optimal control problem for the Ito diffusion process and the controlled linear output with a quadratic quality criterion, an intermediate result is resumed: for approximate calculation of the optimal solution, an alternative to classical numerical integration method based on computer simulation is proposed.
The method allows applying statistical estimation to determine the coefficients @t(y) and Yt(y) of the previously obtained Bellman function Vt(y, z) = atz2 + â(y)z + Yt(y), determining the optimal solution in the original problem of optimal stochastic control. The method is implemented on the basis of the properties of linear parabolic partial differential equations describing @t(y) and Yt(y)  their equivalent description in the form of stochastic differential equations and a theoreticalprobability representation of the solution, known as A. N. Kolmogorov equation, or an equivalent integral form known as the FeynmanKatz formula. Stochastic equations, relations for optimal control and for auxiliary parameters are combined into one differential system, for which an algorithm for simulating a solution is stated. The algorithm provides the necessary samples for statistical estimation of the coefficients â (y) and yt(y). The previously performed numerical experiment is supplemented by calculations presented by an alternative method and a comparative analysis of the results.
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[+] About this article
Title
STOCHASTIC DIFFERENTIAL SYSTEM OUTPUT CONTROL BY THE QUADRATIC CRITERION. IV. ALTERNATIVE NUMERICAL DECISION
Journal
Informatics and Applications
2020, Volume 14, Issue 1, pp 2430
Cover Date
20200330
DOI
10.14357/19922264200104
Print ISSN
19922264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
stochastic differential equation; optimal control; Bellman function; linear differential equations of parabolic type; Kolmogorov equation; FeynmanKatz formula; computer simulations; MonteCarlo method
Authors
A. V. Bosov and A. I. Stefanovich
Author Affiliations
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 442 Vavilov Str., Moscow 119333, Russian Federation
