Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/65365
Title: Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems
Authors: Sun, J
Li, X 
Yong, J
Keywords: Closed-loop solvability
Finiteness
Linear quadratic optimal control
Open-loop solvability
Riccati equation
Stochastic differential equation
Issue Date: 2016
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on control and optimization, 2016, v. 54, no. 5, p. 2274-2308 How to cite?
Journal: SIAM journal on control and optimization 
Abstract: This paper is concerned with a stochastic linear quadratic (LQ) optimal control problem. The notions of open-loop and closed-loop solvabilities are introduced. A simple example shows that these two solvabilities are different. Closed-loop solvability is established by means of solvability of the corresponding Riccati equation, which is implied by the uniform convexity of the quadratic cost functional. Conditions ensuring the convexity of the cost functional are discussed, including the issue of how negative the control weighting matrix-valued function R(•) can be. Finiteness of the LQ problem is characterized by the convergence of the solutions to a family of Riccati equations. Then, a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem, is constructed. Finally, some illustrative examples are presented.
URI: http://hdl.handle.net/10397/65365
ISSN: 0363-0129
EISSN: 1095-7138
DOI: 10.1137/15M103532X
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