广义贴现的长期冲动控制

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-03-04 DOI:10.1137/23m1582539

Damian Jelito, Łukasz Stettner

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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 853-876 页，2024 年 4 月。摘要本文研究了对费勒-马尔科夫过程的长期脉冲控制问题应用广义（非指数）贴现的影响。我们证明，贴现问题的最优值与未贴现问题的最优值相同。接下来，我们证明了未贴现离散时间函数的最优策略也是离散时间贴现准则的最优策略，并且接近连续时间贴现准则的最优策略。这表明，贴现问题在本质上是时间不一致的，但它有一个时间一致的解。此外，我们还可以考虑与时间无关的简单版本，而不是复杂的与时间有关的贝尔曼方程。

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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Long-Run Impulse Control with Generalized Discounting

SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 853-876, April 2024.
Abstract. In this paper, we investigate the effects of applying generalized (nonexponential) discounting on a long-run impulse control problem for a Feller–Markov process. We show that the optimal value of the discounted problem is the same as the optimal value of its undiscounted version. Next, we prove that an optimal strategy for the undiscounted discrete-time functional is also optimal for the discrete-time discounted criterion and nearly optimal for the continuous-time discounted one. This shows that the discounted problem, being time-inconsistent in nature, admits a time-consistent solution. Also, instead of a complex time-dependent Bellman equation, one may consider its simpler time-independent version.

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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.