Several Problems of Stochastic Optimal Controls in Infinite Time Horizon
无限时间范围内随机最优控制的几个问题
基本信息
- 批准号:2305475
- 负责人:
- 金额:$ 25.41万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2023
- 资助国家:美国
- 起止时间:2023-07-01 至 2026-06-30
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
Optimal control theory deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. Optimal control problems are often encountered in engineering and in physical, economic, and social sciences. Examples of optimal control problems include how to control the firing of rocket thrusters to reach a selected target with minimum fuel expenditure, or how to implement monetary policy to minimize unemployment. The underlying mathematical difficulties of the theory are compounded when the time interval for the problem under consideration becomes infinite, and uncertainties, i.e., stochastic effects, need to be accounted for. This project will study stochastic optimal control problems with infinite horizon and extend the knowledge in the field through the introduction of significant extensions of current models to incorporate new effects, and also new models, both of which necessitate new ideas and approaches for their analysis. The project will also provide opportunities for the involvement of undergraduate and graduate students in this research. This project will investigate several important aspects of stochastic optimal control problems with infinite horizon, including: (i) Optimal control of linear stochastic differential equations (SDEs) having mean-field and involving average quadratic costs, via invariant measures; (ii) Turnpike properties of stochastic optimal controls for SDEs; (iii) maximum principle of stochastic optimal controls in infinite horizon for SDEs and for stochastic Volterra integral equations (SVIEs); (iv) Time-inconsistent optimal controls over infinite time horizon for SDEs. These problems necessitate the re-examination of old approaches and development of new tools to expand the scope and enrich the field of optimal control theory.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
最优控制理论研究动态系统在一段时间内的控制,从而使目标函数最优化。最优控制问题在工程以及物理、经济和社会科学中经常遇到。最优控制问题的例子包括如何控制火箭推进器的发射,以最小的燃料支出达到选定的目标,或者如何实施货币政策以将失业率降至最低。当所考虑的问题的时间间隔变得无限大,并且需要考虑不确定性,即随机效应时,该理论潜在的数学困难变得更加复杂。这个项目将研究无限范围的随机最优控制问题,并通过引入现有模型的重大扩展来纳入新的影响和新的模型来扩展该领域的知识,这两个模型都需要新的思想和方法来分析它们。该项目还将为本科生和研究生参与这项研究提供机会。本项目将研究无限范围随机最优控制问题的几个重要方面,包括:(I)具有平均场且涉及平均二次成本的线性随机微分方程(SDE)的最优控制,通过不变度量;(Ii)随机最优控制的收费站性质;(Iii)无限范围内随机最优控制的极大值原理;(Iv)无限时间范围内随机最优控制的时间不一致。这些问题需要重新审查旧的方法和开发新的工具,以扩大范围和丰富最优控制理论的领域。该奖项反映了NSF的法定使命,并通过使用基金会的智力优势和更广泛的影响审查标准进行评估,被认为值得支持。
项目成果
期刊论文数量(5)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Present-biased lobbyists in linear–quadratic stochastic differential games
- DOI:10.1007/s00780-023-00519-9
- 发表时间:2023-04
- 期刊:
- 影响因子:1.7
- 作者:A. Lazrak;Hanxiao Wang;J. Yong
- 通讯作者:A. Lazrak;Hanxiao Wang;J. Yong
Spike Variations for Stochastic Volterra Integral Equations
- DOI:10.1137/22m1522097
- 发表时间:2022-05
- 期刊:
- 影响因子:0
- 作者:Tianxiao Wang;J. Yong
- 通讯作者:Tianxiao Wang;J. Yong
Turnpike Properties for Mean-Field Linear-Quadratic Optimal Control Problems
- DOI:10.1137/22m1524187
- 发表时间:2022-09
- 期刊:
- 影响因子:0
- 作者:Jingrui Sun;J. Yong
- 通讯作者:Jingrui Sun;J. Yong
Linear-Quadratic Optimal Controls for Stochastic Volterra Integral Equations: Causal State Feedback and Path-Dependent Riccati Equations
- DOI:10.1137/22m1492696
- 发表时间:2022-04
- 期刊:
- 影响因子:0
- 作者:Hanxiao Wang;J. Yong;Chao Zhou
- 通讯作者:Hanxiao Wang;J. Yong;Chao Zhou
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Jiongmin Yong其他文献
Regularity Analysis for an Abstract System of Coupled Hyperbolic and Parabolic Equations
双曲和抛物型耦合方程抽象方程组的正则分析
- DOI:
10.1016/j.jde.2015.06.010 - 发表时间:
2014-04 - 期刊:
- 影响因子:2.4
- 作者:
Jianghao Hao;Zhuangyi Liu;Jiongmin Yong - 通讯作者:
Jiongmin Yong
Social Optima in Mean Field Linear-Quadratic-Gaussian Control with Volatility Uncertainty
具有波动性不确定性的平均场线性二次高斯控制的社会最优
- DOI:
10.1137/19m1306737 - 发表时间:
2019-12 - 期刊:
- 影响因子:2.2
- 作者:
Jianhui Huang;Bing-Chang Wang;Jiongmin Yong - 通讯作者:
Jiongmin Yong
Stochastic linear-quadratic optimal control problems with random coefficients: Closed-Loop Representation of Open-Loop Optimal Controls
具有随机系数的随机线性二次最优控制问题:开环最优控制的闭环表示
- DOI:
- 发表时间:
2018 - 期刊:
- 影响因子:0
- 作者:
Jingrui Sun;Jie Xiong;Jiongmin Yong - 通讯作者:
Jiongmin Yong
Representation of Ito integrals by Lebesgue/Bochner integrals
用 Lebesgue/Bochner 积分表示 Ito 积分
- DOI:
10.4171/jems/347 - 发表时间:
2012 - 期刊:
- 影响因子:0
- 作者:
Qi Lü;Jiongmin Yong;Xu Zhang - 通讯作者:
Xu Zhang
Turnpike Properties for Stochastic Linear-Quadratic Optimal Control Problems
随机线性二次最优控制问题的收费公路特性
- DOI:
10.1007/s11401-022-0374-x - 发表时间:
2022-02 - 期刊:
- 影响因子:0
- 作者:
Jingrui Sun;Hanxiao Wang;Jiongmin Yong - 通讯作者:
Jiongmin Yong
Jiongmin Yong的其他文献
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{{ truncateString('Jiongmin Yong', 18)}}的其他基金
Time-Consistency Theory for Time-Inconsistent Stochastic Optimal Control Problems
时间不一致随机最优控制问题的时间一致性理论
- 批准号:
1812921 - 财政年份:2018
- 资助金额:
$ 25.41万 - 项目类别:
Standard Grant
Time-Inconsistent Optimal Control Problems for Stochastic Differential Equations
随机微分方程的时间不一致最优控制问题
- 批准号:
1406776 - 财政年份:2014
- 资助金额:
$ 25.41万 - 项目类别:
Standard Grant
Optimal Control Problems with Time-Inconsistency and Related Topics
时间不一致的最优控制问题及相关主题
- 批准号:
1007514 - 财政年份:2010
- 资助金额:
$ 25.41万 - 项目类别:
Standard Grant
Optimal Control for Forward-Backward Stochastic Differential Equations and Related Topics
前向-后向随机微分方程的最优控制及相关主题
- 批准号:
0604309 - 财政年份:2006
- 资助金额:
$ 25.41万 - 项目类别:
Standard Grant
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