Open-Loop And Closed-Loop Solvabilities For Stochastic Linear Quadratic Optimal Control Problems

Keywords

Closed-loop solvability; Finiteness; Linear quadratic optimal control; Open-loop solvability; Riccati equation; Stochastic differential equation

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.

Publication Date

1-1-2016

Publication Title

SIAM Journal on Control and Optimization

Volume

54

Issue

5

Number of Pages

2274-2308

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1137/15M103532X

Socpus ID

84992648248 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84992648248

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