Indefinite Backward Stochastic Linear-Quadratic Optimal Control Problems

Author:

Sun Jingrui,Wu Zhen,Xiong Jie

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 presented 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.

Funder

National Natural Science Foundation of China

Southern University of Science and Technology

Basic and Applied Basic Research Foundation of Guangdong Province

Natural Science Foundation of Shandong Province

Taishan Scholar Foundation of Shandong Province

Shenzhen Fundamental Research General Program

National Key R&D Program of China

Publisher

EDP Sciences

Subject

Computational Mathematics,Control and Optimization,Control and Systems Engineering

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