STOCHASTIC LINEAR-QUADRATIC OPTIMAL CONTROL WITH PARTIAL OBSERVATION

Sun，Jingrui1; Xiong，Jie2

2023

10.1137/21M146586

SIAM Journal on Control and Optimization   Impact Factor & Quartile

0363-0129

1095-7138

This paper studies a class of quadratic optimal control problems for partially observable linear dynamical systems. In contrast to the full information case, the control is required to be adapted to the filtration generated by the observation system, which in turn is influenced by the control. The variation method fails in this case due to the fact that the filtration is not fixed. To overcome the difficulty, we use the orthogonal decomposition of the state process to write the cost functional as the sum of two parts: one is a functional of the control and the filtering process and the other part is independent of the choice of the control. The first part possesses a mathematical structure similar to the full information problem. By completing the square, it is shown that the open-loop optimal control is given by a feedback representation via the filtering process. The optimal value is also obtained explicitly.

filtering linear-quadratic observation process optimal control Riccati equation

SCI

English

First

National Natural Science Foundation of China[11831010];National Natural Science Foundation of China[11901280];National Natural Science Foundation of China[12271242];Basic and Applied Basic Research Foundation of Guangdong Province[2021A1515010031];National Natural Science Foundation of China[61873325];

Automation & Control Systems ; Mathematics

Automation & Control Systems ; Mathematics, Applied

WOS:001031998600005

SIAM PUBLICATIONS

ENGINEERING

2-s2.0-85165735525

Scopus

1.Department of Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China
2.Department of Mathematics,SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China

Sun，Jingrui,Xiong，Jie. STOCHASTIC LINEAR-QUADRATIC OPTIMAL CONTROL WITH PARTIAL OBSERVATION[J]. SIAM Journal on Control and Optimization,2023,61(3):1231-1247.

Sun，Jingrui,&Xiong，Jie.(2023).STOCHASTIC LINEAR-QUADRATIC OPTIMAL CONTROL WITH PARTIAL OBSERVATION.SIAM Journal on Control and Optimization,61(3),1231-1247.

Sun，Jingrui,et al."STOCHASTIC LINEAR-QUADRATIC OPTIMAL CONTROL WITH PARTIAL OBSERVATION".SIAM Journal on Control and Optimization 61.3(2023):1231-1247.