分数阶时滞微分系统的控制问题研究

In recent years, many fractional differential systems with time delay have been derived from the study for modern control theory and control engineering. The study for some control prblems of such systems have attrated many scholars and become a hot issue. By using the theory of functional differential system and fractional functional differential system, our projet is major to study some control problems of fractional differential systems with time delay. We will focus on time delay and reveal it's impact on fractional differential contol system. Firstly,we will give the distribution of eigenvalue for some kinds of fractional differential system with time delay. Secondly, we will give some results on the stability and stabilization of fractional differential system with time delay. Thirdly, we will deal with the controllability,observability, optimal control and observers design for fractional differential system with time delay and give some relative conclusions. This project considers fractional and time delay factors in control system ,and at the same time, the random and singular factors are also be investigated. We will do our best to make the systems we research in this project more accurate to describe actual systems, this effort will make the results of this project have important actual using value. The systems we research in this project are very complicated control systems, so the problems we will resolve have more deeply theoretical profundity.

近年来，在现代控制理论与控制工程的研究中，导出了许多具有时滞的分数阶微分系统,对该类系统的一些控制问题的研究已引起了国内外许多学者的极大兴趣并成为热点问题。本项目将用泛函微分系统和分数阶微分系统理论，研究具有时滞的分数阶微分系统的若干控制问题。充分考虑时滞因素，揭示时滞对分数阶微分控制系统的影响。我们将给出各种类型分数阶时滞微分系统的特征根的分布；就分数阶时滞微分系统的稳定性和镇定得到一些结果；研究分数阶时滞系统的能控性、能观性、最优控制与观测器设计问题，并给出相关结论。在充分考虑控制系统的分数阶、时滞等因素的同时，也在一些研究中考虑随机和退化因素。力求所讨论的系统能够更加精确地描述实际系统，从而使所得的结果在应用方面具有重要价值。项目研究的系统是非常复杂的控制系统，所要解决的问题较有理论深度。

本项目主要研究具有时滞的分数阶微分系统的若干控制问题，充分考虑时滞因素，揭示时滞对分数阶微分控制系统的影响。我们给出了一些类型分数阶时滞微分系统的特征根分布及解的表示；就分数阶时滞微分系统的稳定性和镇定得到了一些结果；关于分数阶时滞系统的能控性、能观性、最优控制与观测器设计问题，给出了一些结论。发表并标注相关论文78篇; 培养博士研究生8人，硕士研究生38人。本项目所得的结果对泛函微分方程理论的发展具有重要的理论意义；同时由于所研究的系统能够更加精确地描述实际系统，在应用方面也具有重要价值。本项目的研究，在很大程度上提高了我们科研水平，加强了与国内外专家的合作交流。