A switching control strategy for policy selection in stochastic Dynamic Programming problems

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

Automatica Pub Date : 2024-09-05 DOI:10.1016/j.automatica.2024.111884

Massimo Tipaldi , Raffaele Iervolino , Paolo Roberto Massenio , David Naso

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引用次数: 0

Abstract

This paper presents a switching control strategy as a criterion for policy selection in stochastic Dynamic Programming problems over an infinite time horizon. In particular, the Bellman operator, applied iteratively to solve such problems, is generalized to the case of stochastic policies, and formulated as a discrete-time switched affine system. Then, a Lyapunov-based policy selection strategy is designed to ensure the practical convergence of the resulting closed-loop system trajectories towards an appropriately chosen reference value function. This way, it is possible to verify how the chosen reference value function can be approached by using a stabilizing switching signal, the latter defined on a given finite set of stationary stochastic policies. Finally, the presented method is applied to the Value Iteration algorithm, and an illustrative example of a recycling robot is provided to demonstrate its effectiveness in terms of convergence performance.

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随机动态编程问题中政策选择的切换控制策略

本文提出了一种开关控制策略，作为在无限时间范围内随机动态编程问题中选择策略的标准。具体而言，本文将用于迭代求解此类问题的贝尔曼算子推广到随机策略的情况中，并将其表述为离散时间切换仿射系统。然后，设计了一种基于 Lyapunov 的策略选择策略，以确保所得到的闭环系统轨迹朝着适当选择的参考值函数实际收敛。通过这种方法，可以验证如何利用稳定开关信号接近所选的参考值函数，后者定义在给定的有限静态随机策略集合上。最后，介绍的方法被应用于价值迭代算法，并提供了一个回收机器人的示例来证明其收敛性能的有效性。

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.