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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 |
Issue Date: | 2016 | Source: | SIAM journal on control and optimization, 2016, v. 54, no. 5, p. 2274-2308 | 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. | Keywords: | Closed-loop solvability Finiteness Linear quadratic optimal control Open-loop solvability Riccati equation Stochastic differential equation |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on control and optimization | ISSN: | 0363-0129 | EISSN: | 1095-7138 | DOI: | 10.1137/15M103532X | Rights: | © 2016 Society for Industrial and Applied Mathematics The following publication Sun, J., Li, X., & Yong, J. (2016). Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems. SIAM Journal on Control and Optimization, 54(5), 2274-2308 is available at https://doi.org/10.1137/15M103532X |
| Appears in Collections: | Journal/Magazine Article |
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| 15m103532x.pdf | 332.02 kB | Adobe PDF | View/Open |
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