Lur'e型微分包含系统的新型观测器设计研究

In the research of real control systems, uncertainty has become an unavoidable problem during the design procedure. Since differential inclusion has many advantages in describing the uncertain system, the research of differential inclusion has been paid much attention. The novel observer design method for the Lur'e differential inclusion system is mainly studied in this project. Different from the current work on observer design for the Lur'e differential inclusion system, the characteristic of the proposed observer in this project lies that it does not contain any set-valued function. The contents include that, the new observer is designed for the Lur'e differential inclusion system by the filtered transformation approach and the theory of observer, the novel adaptive observer for the Lur'e differential inclusion system is presented by the theory of adaptive observer, the novel interval observer for the Lur'e differential inclusion system is designed by the theory of positive system, and the effectiveness of the designed observers is verified by the motor rotor system. The project may not only overcome some defects existing in the current observer design method for the Lur'e differential inclusion system, but also improve the theory of observer design for the differential inclusion system.

在实际控制系统的研究中，不确定性已经成为了设计过程中不可逃避的问题。由于微分包含在刻画不确定系统方面具有诸多优势，因此受到了控制界广泛的重视。本项目主要研究Lur'e型微分包含系统的新型观测器的设计问题。区别于以往的工作，该类观测器的特点在于不含有集合值函数。研究内容包括：基于滤波变换方法和观测器理论设计出Lur'e型微分包含系统的新型观测器；利用自适应观测器理论给出Lur'e型微分包含系统的新型自适应观测器设计方法；应用正系统理论设计出Lur'e型微分包含系统的新型区间观测器；利用电动机转子系统来检验所设计观测器的有效性。本项目的研究成果有望克服当前Lur'e型微分包含系统的观测器设计方法中的一些缺陷，有助于完善微分包含系统的观测器设计理论。

本项目主要研究Lur'e型微分包含系统的观测器设计问题。所取得的成果主要集中在三个方面。第一，针对Lur'e型微分包含系统，我们建立了新型观测器。主要内容包括：利用滤波变化以及观测器理论，设计出了Lur'e型微分包含系统的新型渐近观测器；基于自适应观测器理论，给出了Lur'e型微分包含系统的新型自适应观测器设计形式。第二，针对含有单边Lipschitz项的Lur'e型微分包含系统，我们给出了新型观测器设计方法。主要内容包括：结合S方法以及自适应观测器理论，我们给出了含有单边Lipschitz项的Lur'e型微分包含系统的自适应全维以及降维观测器的设计形式；基于奇异系统理论，我们设计出了含有单边Lipschitz项的奇异Lur'e型微分包含系统的H无穷观测器。第三，基于所设计的观测器，我们研究了Lur'e型微分包含系统的同步以及镇定设计方法。主要内容包括：利用自适应观测器，我们设计出了Lur'e型微分包含系统的自适应同步算法；基于非脆弱观测器，我们给出了Lur'e型微分包含系统的自适应非脆弱同步设计方法；利用降维观测器，我们提出了Lur'e型微分包含系统的镇定控制器的设计方法。在转子系统的实际背景下，本项目所取得的结果均得到了仿真实验验证。本项目的完成不仅克服了当前Lur'e型微分包含系统观测器的设计缺陷，而且一定程度上完善了微分包含系统的观测器设计理论。