含随机时滞、分布式时滞的分数阶非线性系统鲁棒稳定性及控制

项目名称： 含随机时滞、分布式时滞的分数阶非线性系统鲁棒稳定性及控制

项目编号： No.61304062

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： 赵灵冬

作者单位： 南通大学

项目金额： 24万元

中文摘要： 针对分数阶微积分相对于整数阶微积分在非线性控制领域的突出优势，然而由于分数阶微积分理论复杂和起步较晚，分数阶稳定性理论尤其是含随机时滞、分布式时滞的自治、非自治分数阶非线性系统稳定性理论尚难以满足分数阶系统控制领域发展需要这一现状，本项目拟结合分数阶非线性系统、线性系统稳定性理论研究新的分数阶时滞非线性系统稳定性理论并用多种控制器设计方法实现分数阶非线性系统控制。 新建立的分数阶时滞系统稳定性理论本身简单易懂，基于该系列理论，控制器设计简单，多种整数阶控制器设计方法可拓展应用于分数阶系统；由于干扰分数阶系统系数和微分阶次在一定范围内发生摄动时，该系列理论仍然能用于指导控制器设计实现分数阶系统控制；含随机时滞分数阶非线性系统稳定性理论具有时滞无关的特点。该系列理论和控制方法的研究有助于分数阶控制理论的发展，推动分数阶微积分在时滞非线性系统工程控制中的应用。

中文关键词： 稳定；鲁棒；分数阶；随机时滞；分布式时滞

英文摘要： Though the fractional differentiation is obviously perior to the integer differentiation in nonlinear control area,the stability theorems about fractional system can't meet the development demand of controlling fractinal system,especially fractional autonomous and unautonomous nonlinear system with stochastic delay and distributed delay oweing to the development and the complexity of fractional differentiation.In view of this status,the stability theorems of fractional autonomous and unautonomous nonlinear system with stochastic delay and distributed delay are planed to study based on the stability theorems of fractional nonlinear system and linear system, and study how to design a controller to realize controlling fractional nonlinear system with stochastic delay and distributed delay by many approach in this project. The proposed novel methods not only should be simple and easy to unstand, but also the process of designing controller is easy and the designed controller is easily realized in engineering.Many approaches used in integer system can be extended to control fractional system. The method has a prominent advantage: a fractional system can be controlled when the parameters or fractional order of the fractional system fluctuate in a certain range. The delay-independent conditions can also be derived

英文关键词： stability；robust；fractional；stochastic delay；distributed delay