部分信息线性二次型随机最优控制问题的弱闭环可解性

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-04-27 DOI:10.1007/s00245-025-10262-6

Xun Li, Guangchen Wang, Jie Xiong, Heng Zhang

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引用次数: 0

摘要

研究了一类具有部分信息的线性二次型随机最优控制问题。首先，通过引入两个Riccati方程和一个倒向随机微分方程（BSDE），在标准正半定假设下求解了LQSOC问题。其次，利用摄动方法研究了代价泛函中权矩阵不定时该问题的开环可解性。第三，研究了该问题的弱闭环可解性，证明了开环可解性与弱闭环可解性的等价性。最后，我们给出了一个例子来说明如何获得一个弱闭环最优策略。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Weak Closed-Loop Solvability of Linear Quadratic Stochastic Optimal Control Problems with Partial Information

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.

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.