Analysis, Simulation, and Applications of Stochastic Systems

随机系统的分析、仿真和应用

基本信息

批准号：
2114649
负责人：
Gang George Yin
金额：
$ 52万
依托单位：
University of Connecticut
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-01-15 至 2023-01-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2114649&HistoricalAwards=false
关键词：
Analysis Simulation Applications Stochastic Systems

项目摘要

Stochastic systems are systems in which random disturbances play a significant role. Stemming from emerging and existing applications in networked systems, wireless communications, signal processing, economics, and ecology, this project encompasses the study of dynamically evolving stochastic systems with uncertainties, switching among different configurations, and complex structures. The networked systems of interest include financial, communication, social, biological, and ecological networks. The work will be devoted to learning the intrinsic properties of stochastic network systems, developing mathematical models and novel mathematical methods for analyzing such systems, and designing efficient computational schemes for optimization and control of such systems to meet desired goals. The results of the research will be useful for applications to economics, nonlinear system identification and estimation, un-manned vehicles and other multi-agent systems, biodiversity in ecological systems, and social networks. This projects will involve undergraduate and graduate students and will integrate the research with teaching and student training. This work will contribute jointly to the further development of mathematical theory, computational methods and applications, and the improvement of mathematics education. Motivated by a wide variety of applications, this project will study the following research topics. (1)Stochastic models with random switching will be developed and analyzed. Novel features of the systems include (i) past-dependent switching having a countable state space, and (ii) switching jump diffusions with non-local operators, finite switching set, and sigma finite jump measures. Criteria for recurrence, positive recurrence, and ergodicity will be obtained. (2) Kolmogorov-type systems under white noise perturbations, where the diffusions are degenerate, will be investigated. Applications to control dependent environmental protection zones, infectious disease and ecology will be studied. (3) New algorithms for switching diffusions and stochastic approximation will be developed and their rates of convergence will be studied. (i) For Milstein-type algorithms for solutions of switching diffusions, it will be shown that the algorithms preserve order 1 convergence rates as their diffusion counterpart. (ii) Motivated by applications to multi-agent systems, consensus, and swarming, the novelties of the stochastic approximation algorithms include the inclusion of state-dependent switching, state-dependent observation noise, and general time-dependent nonlinear functions. (4) Precise error estimates for identification of Hammerstein nonlinear systems with quantized observations will be obtained. It will be proved that the estimates escape from a small neighborhood of the true parameter with a probability that is exponentially small. (5) Accurate error bounds for approximation schemes of duplication-deletion random networks in the sense of strong approximation will be obtained. This will have impact on the study of random dynamic graphs and applications to social networks. Extensive numerical experiments and simulations will be performed to complement the analysis and algorithm design. The projects will involve the participation of undergraduate and graduate students.

随机系统是随机干扰起着重要作用的系统。该项目源于网络系统，无线通信，信号处理，经济学和生态学中的新兴和现有应用，该项目涵盖了动态发展具有不确定性的动态发展随机系统的研究，在不同的配置之间切换以及复杂的结构。感兴趣的网络系统包括财务，沟通，社会，生物学和生态网络。这项工作将致力于学习随机网络系统的内在属性，开发数学模型和新的数学方法，用于分析此类系统，并设计有效的计算方案，以优化和控制此类系统以实现所需的目标。该研究的结果将对用于经济学，非线性系统识别和估计，无人驾驶汽车以及其他多机构系统，生态系统中的生物多样性以及社交网络的应用很有用。该项目将涉及本科生和研究生，并将研究与教学和学生培训相结合。这项工作将共同有助于进一步发展数学理论，计算方法和应用以及进步数学教育。受各种应用程序的启发，该项目将研究以下研究主题。（1）将开发和分析具有随机切换的随机模型。系统的新功能包括（i）具有可数的状态空间的过去依赖性切换，以及（ii）与非本地运算符的开关跳转扩散，有限的开关集和Sigma有限的跳跃措施。将获得复发，正复发和终身制的标准。（2）将研究散射散布的白噪声扰动下的kolmogorov型系统。将研究控制依赖环境保护区，传染病和生态学的应用。（3）将开发用于开关扩散和随机近似的新算法，并将研究其收敛速率。（i）对于米尔斯坦型算法，用于开关扩散的溶液，将表明该算法将命令1收敛速率保留为扩散率。（ii）由应用于多代理系统，共识和蜂拥而至的动机，随机近似算法的新颖性包括包括国家依赖性切换，国家依赖性观察噪声以及一般时间依赖时间的非线性函数。（4）将获得具有量化观察结果的Hammerstein非线性系统鉴定的精确误差估计。可以证明，估计值从真实参数的一个小邻居中逸出，概率呈指数较小。（5）将在强近似意义上获得重复删除随机网络的近似值方案的准确误差界。这将影响对社交网络的随机动态图和应用程序的研究。将进行广泛的数值实验和模拟，以补充分析和算法设计。这些项目将涉及本科生和研究生的参与。