Informatics and Applications
2018, Volume 12, Issue 3, pp 99-106
STOCHASTIC DIFFERENTIAL SYSTEM OUTPUT CONTROL BY THE QUADRATIC CRITERION. I. DYNAMIC PROGRAMMING OPTIMAL SOLUTION
- A. V. Bosov
- A. I. Stefanovich
Abstract
The problem of optimal control for the Ito diffusion process and a controlled linear output is solved. The considered statement is close to the classical linear-quadratic Gaussian control (LQG control) problem. Differences consist in the fact that the state is described by the nonlinear differential Ito equation dyy = At(yt) dt + >t(yt) dvt and does not depend on the control ut, optimization subject is controlled linear output dzt = atyt dt + btzt dt + ct ut dt + at dwt. Additional generalizations are included in the quadratic quality criterion for the purpose of statement such problems as state tracking by output or a linear combination of state and output tracking by control. The method of dynamic programming is used for the solution. The assumption about Bellman function in the form Vt(y, z) = atz2 + @t(y)z + Yt(y) allows one to find it. Three differential equations for the coefficients at, @t(y), and Yt(y) give the solution. These equations constitute the optimal solution of the problem under consideration.
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[+] About this article
Title
STOCHASTIC DIFFERENTIAL SYSTEM OUTPUT CONTROL BY THE QUADRATIC CRITERION. I. DYNAMIC PROGRAMMING OPTIMAL SOLUTION
Journal
Informatics and Applications
2018, Volume 12, Issue 3, pp 99-106
Cover Date
2018-08-30
DOI
10.14357/19922264180314
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
stochastic differential equation; optimal control; dynamic programming; Bellman function; Riccati equation; linear differential equations of parabolic type
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, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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