General indefinite backward stochastic linear-quadratic optimal control problems

Sun, Jingrui1; Wen, Jiaqiang1; Xiong, Jie1,2

2022-06-02

10.1051/cocv/2022030

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS   影响因子和分区

1292-8119

1262-3377

A general backward stochastic linear-quadratic optimal control problem is studied, in which both the state equation and the cost functional contain the nonhomogeneous terms. The main feature of the problem is that the weighting matrices in the cost functional are allowed to be indefinite, and the cross-product terms in the control and the state processes are present. Necessary and sufficient conditions for the solvability of the problem are obtained, and a characterization of the optimal control in terms of forward-backward stochastic differential equations is derived. By a Riccati equation approach, a general procedure for constructing optimal controls is developed and the value function is obtained explicitly.

Backward stochastic differential equation linear-quadratic optimal control Riccati equation nonhomo-geneous term

SCI ; EI

英语

第一 ; 通讯

National Natural Science Foundation of China[61873325,11831010] ; Guangdong Basic and Applied Basic Research Foundation[2021A1515010031] ; Natural Science Foundation of Guangdong Province of China[2214050003543] ; SUSTech start-up fund[Y01286120]

Automation & Control Systems ; Mathematics

Automation & Control Systems ; Mathematics, Applied

WOS:000804860000004

EDP SCIENCES S A

20222412212635

Equations of state ; Optimal control systems ; Quadratic programming ; Stochastic control systems ; Stochastic systems

Control Systems:731.1 ; Calculus:921.2 ; Systems Science:961

MATHEMATICS

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China
2.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen 518055, Guangdong, Peoples R China

Sun, Jingrui,Wen, Jiaqiang,Xiong, Jie. General indefinite backward stochastic linear-quadratic optimal control problems[J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS,2022,28.

Sun, Jingrui,Wen, Jiaqiang,&Xiong, Jie.(2022).General indefinite backward stochastic linear-quadratic optimal control problems.ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS,28.

Sun, Jingrui,et al."General indefinite backward stochastic linear-quadratic optimal control problems".ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS 28(2022).