Asymptotic Properties of Integro-differential Systems with Wideband Noise Perturbations

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• 英文论文题名：Asymptotic Properties of Integro-differential Systems with Wideband Noise Perturbations
• 论文作者：Fuke Wu ; George Yin
• 英文论文作者：Fuke Wu ; George Yin ; School of Mathematics and Statistics ; Huazhong University of Science and Technology ; Department of Mathematics ; Wayne State University
• 年：2017
• 作者机构：School of Mathematics and Statistics,Huazhong University of Science and Technology;Department of Mathematics,Wayne State University;
• 英文论文关键词：Integro-differential equations ; Wideband noise ; Perturbed test function ; Weak convergence ; Tightness
• 会议召开时间：2017-07-26
• 会议录名称：第36届中国控制会议论文集（B）
• 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
• 语种：英文
• 分类号：O175
• 学会代码：KZLL
• 会议名称：第36届中国控制会议
• 会议地点：中国辽宁大连
• 主办单位：中国自动化学会控制理论专业委员会
• 学会名称：中国自动化学会控制理论专业委员会
• 页数：6
• 文件大小：213k
• 原文格式：D
• 会议级别：全国

摘要

Because the class of wideband noise is quite realistic in applications and is a good approximation to white noise, this paper focuses on the asymptotic properties of integro-differential systems with wideband noise perturbations. Using perturbed test function methods combined with the martingale averaging techniques, and weak convergence methods, it is shown that when the small parameter tends to zero, the underlying process converges weakly to a stochastic process satisfying a stochastic integro-differential equation. Inspired by the developments from [3] and [9], the novelty of our paper lies in the treatment of functional differential equations in which differential-integral equations are dealt with. Because of the features of the systems involved, different methods for estimates and proofs from the aforementioned references are developed in this paper. Not only are the results interesting from a mathematical point of view, but also they will be of great utility to a wide range of problems in control and optimization problems.
Because the class of wideband noise is quite realistic in applications and is a good approximation to white noise, this paper focuses on the asymptotic properties of integro-differential systems with wideband noise perturbations. Using perturbed test function methods combined with the martingale averaging techniques, and weak convergence methods, it is shown that when the small parameter tends to zero, the underlying process converges weakly to a stochastic process satisfying a stochastic integro-differential equation. Inspired by the developments from [3] and [9], the novelty of our paper lies in the treatment of functional differential equations in which differential-integral equations are dealt with. Because of the features of the systems involved, different methods for estimates and proofs from the aforementioned references are developed in this paper. Not only are the results interesting from a mathematical point of view, but also they will be of great utility to a wide range of problems in control and optimization problems.

引文

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