随机控制系统的输入到状态稳定性

项目名称： 随机控制系统的输入到状态稳定性

项目编号： No.61304070

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 自动化技术、计算机技术

项目作者： 刘磊

作者单位： 河海大学

项目金额： 23万元

中文摘要： 在实际的控制系统中，相对于Lyapunov稳定性，研究系统输入、输出和状态变量之间的关系对实现系统控制更为重要，并且当所考虑系统的随机因素不可忽略时，就必须进行随机分析，这就导致了随机输入到状态稳定性的研究。本项目对非线性随机控制系统在p阶矩收敛、几乎必然渐近收敛、依分布收敛意义下的随机输入到状态稳定性进行研究，建立非线性随机控制系统输入到状态稳定的若干理论判据，包括应用Lasalle型方法、Razumikhin 型方法、基于Lyapunov函数的小增益型方法，并结合随机分析的工具讨论非线性随机控制系统输入到状态稳定性。研究白噪声对确定性控制系统的镇定和失稳作用,并讨论随机干扰强度和原确定性系统输入到状态稳定保持和消除的概率之间的量化关系。本项目将深刻揭示随机输入到稳定性的机理，拓广随机输入到状态稳定性的理论与方法，为研究随机控制系统输入到状态稳定提供新思路。

中文关键词： 随机系统；输入到状态稳定性；随机扰动；；

英文摘要： In the actually control system, it is more important to research the relationships among input, output, and state of a system in realizing the control of it.In addition, when the stochastic factors of a system can not be ignored, stochastic analysis on the control system is necessary, which leads to the study of stochastic input-to-state stability.In this project, we will study the input-to-state stability of nonlinear stochastic control systems, and try to establish some theory criterions on such kind of stability, including the discussion of input-to-state stability of nonlinear stochastic control system by using the Lasalle-type theorem, Razumikhin-type theorem and small gain-type theorem based on Lyapunov function. The stochastic stabilization and destabilization by Brownian noise perturbation of nonlinear deterministic differential contor system will be investigated, and the quantitative relationship between the stochastic perturbation intensity and the probability of the maintenance or disappearance of the input-to-state stability will be discussed as well. This work will help to probe the mechanisms of stochastic input-to-state stability. The study of the project will extend the theory and method of stochastic input-to-state stability and initiate the new idea of studying stochastic input-to-state stabil

英文关键词： Stochastic Systems；Input-to-State Stability；Stochastic Perturbation；；