Pontryagin’s Principle for Some Probabilistic Control Problems

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-06-05 DOI:10.1007/s00245-024-10151-4

Wim van Ackooij, René Henrion, Hasnaa Zidani

引用次数: 0

Abstract

In this paper we investigate optimal control problems perturbed by random events. We assume that the control has to be decided prior to observing the outcome of the perturbed state equations. We investigate the use of probability functions in the objective function or constraints to define optimal or feasible controls. We provide an extension of differentiability results for probability functions in infinite dimensions usable in this context. These results are subsequently combined with the optimal control setting to derive a novel Pontryagin’s optimality principle.

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某些概率控制问题的庞特里亚金原理

本文研究的是受随机事件扰动的最优控制问题。我们假设必须在观察扰动状态方程的结果之前决定控制方法。我们研究在目标函数或约束条件中使用概率函数来定义最优或可行控制。我们对无限维概率函数的可微性结果进行了扩展，使其适用于这种情况。随后，我们将这些结果与最优控制设置相结合，推导出一个新颖的庞特里亚金最优性原理。

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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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.