On the properties of monotone functionals for generalizing Bellman Principle

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2025-06-19 DOI:10.1016/j.automatica.2025.112418

Auguste Caen , Jean-Denis Mathias

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引用次数: 0

Abstract

Dynamic programming is classically used for solving optimal control problems. This approach is based on equating the value function of the problem under study as well as the Bellman Principle. However, despite a sharing common framework, each optimal control problem is addressed independently, depending on the characteristics of the cost function. The objective of this article is to establish a unified approach within the context of deterministic, autonomous dynamics with an infinite horizon. The ultimate purpose is to determine conditions from which an optimal control problem admits a Bellman principle. To achieve this, we introduce a typology composed of three so-called monotone functionals, which encompass typical cost functions met in the literature. Any functional that complies with the properties of one of this class can be used for tackling optimal control problems through Bellman principle. Then, we show that classical functionals used in the literature can be classified in one these classes. Finally, we show how to build a functional according to this typology through a simple problem of optimization.

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推广Bellman原理的单调泛函的性质

动态规划是解决最优控制问题的经典方法。这种方法是基于对所研究问题的价值函数的等价以及Bellman原理。然而，尽管有一个共享的公共框架，每个最优控制问题都是独立解决的，这取决于成本函数的特征。本文的目的是在具有无限视界的确定性、自主动力学的背景下建立一种统一的方法。最终目的是确定最优控制问题允许贝尔曼原理存在的条件。为了实现这一目标，我们引入了一个由三个所谓的单调泛函组成的类型学，其中包括文献中遇到的典型成本函数。任何符合这类性质的函数都可以通过Bellman原理来解决最优控制问题。然后，我们证明了文献中使用的经典泛函可以归类为这些类别之一。最后，我们将通过一个简单的优化问题来展示如何根据这种类型构建函数。

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

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.