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

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 based on the stability theorem about fractional system with stochastic delay. Studying the theroems and control approaches is helpful to develop fractional control theorem and promte fractional differentiation to be applied to control nonlinear system with delay in engineering.

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。

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时滞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，本项目结合分数阶非线性系统、线性系统稳定性理论研究了分数阶时滞非线性系统稳定性与控制问题。.构造正定函数及半正定函数并分别求分数阶导数和整数阶导数建立了离散时滞、分布式时滞分数阶系统稳定性理论，利用卷积运算构造新的正定函数将整数阶系统Lyapunov理论拓展到了分数阶时滞系统。设计控制器实现了离散时滞、分布式时滞、混合式时滞分数阶复杂网络同步控制。提出了矩阵配置的控制器设计方法，并将该方法应用于无时滞、离散时滞、分布式时滞、混合时滞的整数阶、分数阶混沌系统同步控制。该控制器设计方法不仅能实现参数已知的混沌系统同步控制，也能实现参数未知的混沌系统参数辨识和自适应同步。.项目构造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直接拓展应用于分数阶系统；微分阶次在（0,1）范围内发生摄动时，该系列理论仍然有效。所建立的控制器设计方法简单，适用，便于在工程中应用。