Indefinite Backward Stochastic Linear-Quadratic Optimal Control Problems
Optimization and Control
2021-04-13 v1
Abstract
This paper is concerned with a backward stochastic linear-quadratic (LQ, for short) optimal control problem with deterministic coefficients. The weighting matrices are allowed to be indefinite, and cross-product terms in the control and state processes are present in the cost functional. Based on a Hilbert space method, necessary and sufficient conditions are derived for the solvability of the problem, and a general approach for constructing optimal controls is developed. The crucial step in this construction is to establish the solvability of a Riccati-type equation, which is accomplished under a fairly weak condition by investigating the connection with forward stochastic LQ optimal control problems.
Cite
@article{arxiv.2104.04747,
title = {Indefinite Backward Stochastic Linear-Quadratic Optimal Control Problems},
author = {Jingrui Sun and Zhen Wu and Jie Xiong},
journal= {arXiv preprint arXiv:2104.04747},
year = {2021}
}
Comments
27 pages