Research on Stochastic Systems and Optimization: Analysis, Algorithms, and Computations

随机系统和优化研究:分析、算法和计算

基本信息

  • 批准号:
    0907753
  • 负责人:
  • 金额:
    $ 30.14万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2009
  • 资助国家:
    美国
  • 起止时间:
    2009-09-01 至 2013-08-31
  • 项目状态:
    已结题

项目摘要

Focusing on new algorithms design for stochastic optimization and investigating basic properties of systems arising in emerging applications, this research project encompasses the following four aspects. (1) It aims to develop stochastic approximation algorithms with Markovian switching and examining Markov modulated random sequences; it reveals asymptotic properties such as limit switching diffusions, large deviations, strong invariance, and ergodicity. (2) It presents numerical methods for solutions of regime-switching stochastic differential equations with continuous-state-depend switching. In addition to convergence, in the second phase, rates of convergence of the algorithms, numerical methods for the related control problems, and their convergence rates are to be investigated. (3) It carries out system identification with Markov parameter and binary-valued or quantized observations. It facilitates the understanding of tractability, complexity, and modeling capability under limited sensor information. (4) It analyzes stability of switching jump diffusions with state-dependent switching, and provides sufficient conditions for stability and instability of nonlinear systems and necessary and sufficient conditions for linearizable systems. Consisting of in-depth analysis and extensive numerical experiments, our goals are to gain new insight, and to advance state of the art of stochastic optimization methods and stochastic systems theory.This research project is motivated by emerging applications arising in wireless communication, adaptive signal processing, production planning, queueing systems, biological, ecological, and economic systems, which are inevitably involve uncertainty. In contrast to the usual models in the existing literature, the systems are often influenced by random environment as well. For example, when two or more species live in proximity and share the same basic requirements, they usually compete for resources, food, habitat, or territory. Traditional models use (either random or non-random) differential equations for such scenarios. However, the systems are often subject to additional environmental noise, which cannot be described by the traditional differential equation setup. Other examples include insurance risk models and ion channel (biological nanotubes) dynamics among others. The proposed project aims to take into such random environment and other uncertain factors into consideration. It presents novel algorithms for optimization tasks, designs numerical procedures for solving systems of equations, carries out identification task for systems with unknown parameters and limited sensor information, and obtains longtime behavior of systems involving both continuous dynamics and discrete events. The models to be examined, the numerical algorithms to be developed, and the insight to be gained will jointly contribute to the field of stochastic optimization and make impact on the aforementioned applications. Several graduate students are involved in the research project. By integrating the proposed research with teaching, the planned work contributes to the further development of stochastic optimization and stochastic systems theory and the improvement of mathematics education.
本研究计画针对随机最佳化的新演算法设计,并探讨新兴应用中所产生的系统基本性质,包含以下四个方面。 (1)它的目的是开发随机近似算法与马尔可夫开关和检查马尔可夫调制的随机序列;它揭示了渐近性质,如极限开关扩散,大偏差,强不变性和遍历性。(2)给出了具有连续状态依赖切换的状态切换随机微分方程的数值解法。除了收敛性,在第二阶段,算法的收敛速度,相关控制问题的数值方法,以及它们的收敛速度将被调查。(3)它利用马尔可夫参数和二值或量化观测值进行系统辨识。它有助于在有限的传感器信息下理解易处理性、复杂性和建模能力。(4)分析了具有状态依赖切换的切换跳跃扩散的稳定性,给出了非线性系统稳定和不稳定的充分条件以及可线性化系统的充要条件. 我们的目标是通过深入的分析和大量的数值实验,获得新的见解,并推进随机优化方法和随机系统理论的最新发展。本研究项目的动机是新兴的应用中出现的无线通信,自适应信号处理,生产计划,生产系统,生物,生态和经济系统,这些都不可避免地涉及不确定性。 与现有文献中常见的模型不同,该系统还经常受到随机环境的影响。 例如,当两个或两个以上的物种生活在一起,并且有着相同的基本需求时,它们通常会争夺资源、食物、栖息地或领土。传统的模型使用(随机或非随机)微分方程的情况下。然而,该系统往往受到额外的环境噪声,这是不能描述的传统的微分方程组。其他例子包括保险风险模型和离子通道(生物纳米管)动力学等。 拟议项目旨在考虑到这种随机环境和其他不确定因素。它提出了新的优化任务的算法,设计数值求解方程组的程序,执行识别任务的系统未知参数和有限的传感器信息,并获得长期的行为系统涉及连续动态和离散事件。 待检查的模型,待开发的数值算法,以及获得的洞察力将共同有助于随机优化领域,并对上述应用产生影响。 几个研究生参与了这个研究项目。 通过将所提出的研究与教学相结合,计划的工作有助于随机优化和随机系统理论的进一步发展和数学教育的改进。

项目成果

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Gang George Yin其他文献

Convergence rates of Markov chain approximation methods for controlled diffusions with stopping
Identification Error Bounds and Asymptotic Distributions for Systems with Structural Uncertainties
  • DOI:
    10.1007/s11424-006-0022-7
  • 发表时间:
    2006-03-01
  • 期刊:
  • 影响因子:
    2.800
  • 作者:
    Gang George Yin;Shaobai Kan;Le Yi Wang
  • 通讯作者:
    Le Yi Wang

Gang George Yin的其他文献

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{{ truncateString('Gang George Yin', 18)}}的其他基金

Collaborative Research: AMPS Stochastic Algorithms for Early Detection and Risk Prediction of Hidden Contingencies in Modern Power Systems
合作研究:用于现代电力系统中隐藏突发事件的早期检测和风险预测的 AMPS 随机算法
  • 批准号:
    2229108
  • 财政年份:
    2022
  • 资助金额:
    $ 30.14万
  • 项目类别:
    Standard Grant
Modeling, Analysis, Optimization, Computation, and Applications of Stochastic Systems
随机系统的建模、分析、优化、计算和应用
  • 批准号:
    2204240
  • 财政年份:
    2022
  • 资助金额:
    $ 30.14万
  • 项目类别:
    Continuing Grant
Analysis, Simulation, and Applications of Stochastic Systems
随机系统的分析、仿真和应用
  • 批准号:
    2114649
  • 财政年份:
    2021
  • 资助金额:
    $ 30.14万
  • 项目类别:
    Continuing Grant
Analysis, Simulation, and Applications of Stochastic Systems
随机系统的分析、仿真和应用
  • 批准号:
    1710827
  • 财政年份:
    2017
  • 资助金额:
    $ 30.14万
  • 项目类别:
    Continuing Grant
Analysis, Algorithm Design, and Computation for Stochastic Systems and Optimization
随机系统和优化的分析、算法设计和计算
  • 批准号:
    1207667
  • 财政年份:
    2012
  • 资助金额:
    $ 30.14万
  • 项目类别:
    Continuing Grant
Stochastic Optimization: Approximation Algorithms and Asymptotic Analysis
随机优化:近似算法和渐近分析
  • 批准号:
    0603287
  • 财政年份:
    2006
  • 资助金额:
    $ 30.14万
  • 项目类别:
    Standard Grant
Recursive Algorithms and Regime Switching Models for Stochastic Optimization
随机优化的递归算法和机制切换模型
  • 批准号:
    0304928
  • 财政年份:
    2003
  • 资助金额:
    $ 30.14万
  • 项目类别:
    Standard Grant
Optimization for Systems Under Uncertainty: Modeling, Asymptotic Analysis, and Recursive Algorithms
不确定性下的系统优化:建模、渐近分析和递归算法
  • 批准号:
    9877090
  • 财政年份:
    1999
  • 资助金额:
    $ 30.14万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Analysis and Numerical Methods in Stochastic Optimization
数学科学:随机优化中的分析和数值方法
  • 批准号:
    9529738
  • 财政年份:
    1996
  • 资助金额:
    $ 30.14万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Studies in Stochastic Optimization
数学科学:随机优化研究
  • 批准号:
    9224372
  • 财政年份:
    1993
  • 资助金额:
    $ 30.14万
  • 项目类别:
    Standard Grant

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Collaborative Research: AMPS Stochastic Algorithms for Early Detection and Risk Prediction of Hidden Contingencies in Modern Power Systems
合作研究:用于现代电力系统中隐藏突发事件的早期检测和风险预测的 AMPS 随机算法
  • 批准号:
    2229108
  • 财政年份:
    2022
  • 资助金额:
    $ 30.14万
  • 项目类别:
    Standard Grant
Collaborative Research: CIF: Small: Nonasymptotic Analysis for Stochastic Networks and Systems: Foundations and Applications
合作研究:CIF:小型:随机网络和系统的非渐近分析:基础和应用
  • 批准号:
    2207547
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    $ 30.14万
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    Standard Grant
Collaborative Research: CIF: Small: Nonasymptotic Analysis for Stochastic Networks and Systems: Foundations and Applications
合作研究:CIF:小型:随机网络和系统的非渐近分析:基础和应用
  • 批准号:
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Collaborative Research: AMPS Stochastic Algorithms for Early Detection and Risk Prediction of Hidden Contingencies in Modern Power Systems
合作研究:用于现代电力系统中隐藏突发事件的早期检测和风险预测的 AMPS 随机算法
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