Dynamic Programming in Probability Spaces via Optimal Transport

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-04-03 DOI:10.1137/23m1560902

Antonio Terpin, Nicolas Lanzetti, Florian Dörfler

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 1183-1206, April 2024.
Abstract. We study discrete-time finite-horizon optimal control problems in probability spaces, whereby the state of the system is a probability measure. We show that, in many instances, the solution of dynamic programming in probability spaces results from two ingredients: (i) the solution of dynamic programming in the “ground space” (i.e., the space on which the probability measures live) and (ii) the solution of an optimal transport problem. From a multi-agent control perspective, a separation principle holds: “low-level control of the agents of the fleet” (how does one reach the destination?) and “fleet-level control” (who goes where?) are decoupled.

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通过最优传输进行概率空间动态编程

SIAM 控制与优化期刊》第 62 卷第 2 期第 1183-1206 页，2024 年 4 月。摘要。我们研究概率空间中的离散时间有限视距最优控制问题，其中系统的状态是一个概率度量。我们证明，在许多情况下，概率空间中动态程序设计的解来自两个方面：(i) "地面空间"（即概率度量所在的空间）中动态编程的求解；(ii) 最佳传输问题的求解。从多代理控制的角度来看，分离原则是成立的："车队代理的低级控制"（如何到达目的地？）和 "车队级控制"（谁去哪里？

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

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.