不确定分数阶模糊时滞系统的分析与综合

项目名称： 不确定分数阶模糊时滞系统的分析与综合

项目编号： No.61203047

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 自动化学科

项目作者： 宋晓娜

作者单位： 河南科技大学

项目金额： 25万元

中文摘要： 分数阶系统是传统整数阶系统的拓展和延伸，它对人们更加精确地认识和描述自然界中的事物起到了重要的作用。目前针对分数阶系统的研究大都集中在分数阶线性系统上，而对于分数阶非线性系统，其稳定性分析和控制器设计问题还没有得到系统深入地研究。项目在借鉴和发掘分数阶系统和模糊时滞系统传统研究思路和方法的基础上，系统完整地探索分数阶模糊时滞系统的分析与综合问题。首先，通过Mittag-Leffler函数、k类函数、Lyapunov稳定性分析理论等方法研究分数阶模糊时滞系统的基于不同性能指标的时滞相关稳定性分析问题；其次，利用鲁棒控制理论、输出反馈控制等综合方法对分数阶模糊时滞系统进行鲁棒输出反馈控制研究，提出控制器设计方法；最后，采用仿真手段验证所设计控制器的有效性，并在此基础上分析控制算法的保守性问题，提出改进方法。可以预期，对于本项目的研究必将拓展分数阶系统和模糊时滞系统的理论研究深度及实际应用范围。

中文关键词： 分数阶模糊系统；时滞系统；稳定性分析；输出反馈控制；自适应滑模控制

英文摘要： Fractional-order (FO) systems are the extension of the traditional integer-order systems, they play a significant role in understanding and describing the nature more accurately. Currently, most of the research for the FO systems are focused on the FO linear systems. However, the stability analysis and controller design problems for FO nonlinear systems still have not studied systematically. Based on the traditional research methods of FO systems and fuzzy time-delay systems, this project investigates the stability analysis and synthesis problems for the FO fuzzy time-delay systems. Firstly, in terms of Mittage-Leffler function, class-k functions, Lyapunov stability analysis theory methods, the delay-dependent conditions of stability analysis for FO fuzzy time-delay systems under some certain performance constraints are obtained; Secondly, using robust control theory, output feedback control synthesis methods, etc., the problem of robust output feedback controller design is discussed for FO fuzzy time-delay systems, and the controller design method is presented; Finally, simulation examples are provided to signify the effectiveness of the proposed control scheme. Based on this, the conservative problem of the controller design method is analysed, and the improved controller design method is provided. We can expe

英文关键词： Fractional order fuzzy systems；Time delay systems；Stability analysis；Output feedback control；Adaptive sliding mode control