Weak Closed-loop Solvability of Linear Quadratic Stochastic Optimal Control Problems with Partial Information
Optimization and Control
2024-09-26 v1
Abstract
This paper investigates a linear quadratic stochastic optimal control (LQSOC) problem with partial information. Firstly, by introducing two Riccati equations and a backward stochastic differential equation (BSDE), we solve this LQSOC problem under standard positive semidefinite assumptions. Secondly, by means of a perturbation approach, we study open-loop solvability of this problem when the weighting matrices in the cost functional are indefinite. Thirdly, we investigate weak closed-loop solvability of this problem and prove the equivalence between open-loop and weak closed-loop solvabilities. Finally, we give an example to illustrate the way for obtaining a weak closed-loop optimal strategy.
Cite
@article{arxiv.2409.16924,
title = {Weak Closed-loop Solvability of Linear Quadratic Stochastic Optimal Control Problems with Partial Information},
author = {Xun Li and Guangchen Wang and Jie Xiong and Heng Zhang},
journal= {arXiv preprint arXiv:2409.16924},
year = {2024}
}