有吸收边界的汉密尔顿-雅各比-贝尔曼方程的马尔可夫链近似法

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS SIAM Journal on Control and Optimization Pub Date : 2024-03-29 DOI:10.1137/23m1565723

Itsuki Watanabe

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引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 2 期第 1152-1164 页，2024 年 4 月。摘要我们考虑了受控马尔可夫过程的无限视界最优控制问题。我们用粘度解法验证了受控马尔可夫过程与其流体极限之间的关系。更确切地说，我们证明了受控马尔可夫过程的值函数收敛于其极限过程之一，即相关汉密尔顿-贾可比-贝尔曼方程的粘性解。

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Markov Chain Approximation for Hamilton–Jacobi–Bellman Equation with Absorbing Boundary

SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 1152-1164, April 2024.
Abstract. We consider the infinite horizon optimal control problems of the controlled Markov process. We verify the relationship between the controlled Markov process and its fluid limit by the viscosity solution approach. More precisely, we show that the value function of the controlled Markov process converges to one of its limit processes which is the viscosity solution of the associated Hamilton–Jacobi–Bellman equation.

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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.