无界可测成分的粘性遍历问题，第 1 部分：HJB 方程

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS SIAM Journal on Control and Optimization Pub Date : 2024-02-01 DOI:10.1137/22m1478069

Hicham Kouhkouh

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引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 1 期第 415-440 页，2024 年 2 月。摘要。我们讨论了在整个空间[math]中[math]形式的[math]遍历汉密尔顿-雅各比-贝尔曼（HJB）方程的解[math]的存在性和唯一性问题，其中[math]是一个贝尔曼汉密尔顿。我们使用的方法与经典方法不同。它依赖于抽象巴拿赫空间中的对偶理论和优化，以及扩散算子的最大耗散性。

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A Viscous Ergodic Problem with Unbounded and Measurable Ingredients, Part 1: HJB Equation

SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 415-440, February 2024.
Abstract. We address the problem of existence and uniqueness of solutions [math] to ergodic Hamilton–Jacobi–Bellman (HJB) equations of the form [math] in the whole space [math] with unbounded and merely measurable data and where [math] is a Bellman Hamiltonian. The method we use is different from classical approaches. It relies on duality theory and optimization in abstract Banach spaces together with maximal dissipativity of the diffusion operator.

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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.