This paper investigates the stochastic linear quadratic (LQ, for short) optimal control problem of Markovian regime switching system. The representation of the cost functional for the stochastic LQ optimal control problem of Markovian regime switching system is derived by the technique of Itô’s formula with jumps. For the stochastic LQ optimal control problem of Markovian regime switching system, we establish the equivalence between the open-loop (closed-loop, resp.) solvability and the existence of an adapted solution to the corresponding forward-backward stochastic differential equation with constraint. (i.e., the existence of a regular solution to Riccati equations). Also, we analyze the interrelationship between the strongly regular solvability of Riccati equations and the uniform convexity of the cost functional. Finally, we present an example which is open-loop solvable but not closed-loop solvable.
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Keywords: Linear quadratic optimal control, markovian regime switching, Riccati equations, open-loop solvability, closed-loop solvability
@article{COCV_2021__27_1_A71_0,
author = {Zhang, Xin and Li, Xun and Xiong, Jie},
title = {Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems of {Markovian} regime switching system},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021066},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021066/}
}
TY - JOUR AU - Zhang, Xin AU - Li, Xun AU - Xiong, Jie TI - Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems of Markovian regime switching system JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021066/ DO - 10.1051/cocv/2021066 LA - en ID - COCV_2021__27_1_A71_0 ER -
%0 Journal Article %A Zhang, Xin %A Li, Xun %A Xiong, Jie %T Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems of Markovian regime switching system %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021066/ %R 10.1051/cocv/2021066 %G en %F COCV_2021__27_1_A71_0
Zhang, Xin; Li, Xun; Xiong, Jie. Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems of Markovian regime switching system. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 69. doi: 10.1051/cocv/2021066
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Cité par Sources :
The first author is supported by National Natural Science Foundation of China (grant no. 11771079) and Fundamental Research Funds for the Central Universities (grant no. 2242021R41082), the second author is supported by RGC Grants (grant nos. 15209614, 15213218 and 15215319) and partially from CAS AMSS-PolyU Joint Laboratory of Applied Mathematics, and the third author is supported by Southern University of Science and Technology Start up fund Y01286120 and National Natural Science Foundation of China (grant nos. 61873325, 11831010).
