变终端时间非凸控制域最优控制问题的随机极大值原理

IF 1.7 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-08-27 DOI:10.1007/s00245-025-10302-1

Jin Shi, Shuzhen Yang

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引用次数: 0

摘要

本文考虑状态约束下随机最优控制问题的变终端时间结构，其中终端时间随状态均值而变化。在这种新的随机最优控制系统中，控制域不需要是凸的，扩散系数中包含控制变量。为了克服相关庞特里亚金随机极大原理的证明困难，我们建立了变终端时间的渐近一阶和二阶伴随方程，并建立了其变分方程。最后，我们通过两个实例验证了本研究的主要结果。

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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Stochastic Maximum Principle for Optimal Control Problem with Varying Terminal Time and Non-convex Control Domain

In this paper, we consider a varying terminal time structure for the stochastic optimal control problem under state constraints, in which the terminal time varies with the mean value of the state. In this new stochastic optimal control system, the control domain does not need to be convex and the diffusion coefficient contains the control variable. To overcome the difficulty in the proof of the related Pontryagin’s stochastic maximum principle, we develop asymptotic first- and second-order adjoint equations for the varying terminal time, and establish its variational equation. In the end, we present two examples to verify the main results of this study.

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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.