A data-driven practical stabilization approach for solving stochastic dynamic programming problems

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

Automatica Pub Date : 2025-05-17 DOI:10.1016/j.automatica.2025.112372

Massimo Tipaldi , Raffaele Iervolino , Paolo Roberto Massenio , Ali Forootani

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引用次数: 0

Abstract

This paper presents a data-driven practical stabilization approach for solving stochastic Dynamic Programming problems with unknown Markov Decision Process models over an infinite time horizon. The Bellman operator is modeled as a discrete-time switched affine system, with each mode representing a specific stationary stochastic policy and an external bounded disturbance term to account for such modeling issue. A two-step approach is followed. First, a model-based robust practical stabilization problem is solved to derive stabilization conditions which enable the practical convergence of the resulting closed-loop system trajectories towards a chosen reference value function. Then, by exploiting recent model-to-data Linear Matrix Inequality transformation tools, these results are further developed to obtain data-driven robust stabilization conditions for addressing the case of model-free problems. Such data-driven stabilization conditions are deployed into the Value Iteration algorithm, and finally tested on the recycling robot and the parking lot management problems to demonstrate the effectiveness of the proposed method.

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随机动态规划问题的数据驱动实用镇定方法

本文提出了一种数据驱动的实用镇定方法，用于解决无限时间范围内未知马尔可夫决策过程模型的随机动态规划问题。Bellman算子被建模为一个离散时间切换仿射系统，每个模式代表一个特定的平稳随机策略和一个外部有界干扰项来解释这种建模问题。遵循两步方法。首先，解决了一个基于模型的鲁棒实际镇定问题，导出了镇定条件，使闭环系统轨迹向选定的参考值函数收敛。然后，利用最近的模型到数据线性矩阵不等式转换工具，进一步发展这些结果，以获得数据驱动的鲁棒镇定条件，用于解决无模型问题。将这种数据驱动的稳定条件部署到值迭代算法中，最后在回收机器人和停车场管理问题上进行了测试，验证了所提方法的有效性。

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.