基于共轭理论的连续T-S模糊系统局部控制研究

In recent years, the research of T-S fuzzy systems is mainly about global property (global stability, stabilization etc.), but most of the results are only sufficient conditions which can not guarantee the global property for some T-S fuzzy systems,on the other hand, there does not exist global property for some nonlinear systems which lead to local T-S fuzzy model, thus it is very necessary to explore local property of the T-S fuzzy systems. Based on the previous work, the aim of this project is to study the local property of nonlinear systems presented as T-S fuzzy model by applying the conjugate theory. Firstly, the local stability and local stabilization will be studied by construsting conjugate function. Compared with the exsiting methods about local fuzzy control, the obtained new results can not only ensure a larger stability region but also can be used to more fuzzy systems. Secondly, the effection of different kinds of disturbances on the stability region will be studied and a new algorithm will be designed to reject the diturbances. Also, the relationship between disturbances and invariant sets will be investigated. Thirdly, for the known premise variables and unknown variables, different local observers will be designed to ensure the stability of the error systems whose initial values will also be discussed and a new method will be proposed to solve the problem. Fourthly, the local stability and stabilization region will be obtained for the T-S fuzzy model with time-delay by defining a new vector norm. In the end, the control system of the permanent magnet synchronous motor with windup will be studied by using the new local fuzzy control methods obtained above. This project will complete and develop the theory of T-S fuzzy systems, and also has good effect on other research areas.

近年来对T-S模糊系统的研究主要集中于全局特性，但由于现有模糊控制方法多为充分条件，有时无法保证模糊系统的全局特性；此外，某些非线性系统本身不具有全局特性，导致所得的模糊系统不具有全局特性，探讨其局部特性成为最近的研究热点之一。本项目拟应用共轭理论研究T-S模糊系统的局部特性。首先，通过构造共轭函数研究模糊系统的局部稳定及镇定，使所得结果不但能够得到更大的局部稳定区域而且应用范围更广；其次，针对不同种类的扰动，设计优化算法抑制其对系统的影响并探明扰动与不变集之间的关系；然后，根据前件变量已知和未知两种情况设计不同的观测器使得误差系统局部稳定，讨论误差系统的初始值与稳定区域的关系并给出解决方法；进一步，通过定义新的向量泛数得到模糊时滞系统的局部稳定区域；最后，将所得结果用于处理含windup现象的永磁同步电机的模糊控制问题。该项目的顺利实施能够完善模糊控制理论，并对其它研究领域产生积极影响。

大部分对T-S模糊系统的研究主要集中于全局特性，但由于现有模糊控制方法多为充分条件，有时无法保证模糊系统的全局特性；此外，某些非线性系统本身不具有全局特性，导致所得的模糊系统不具有全局特性，探讨其局部特性成为最近的研究热点之一。本项目采用新方法研究了T-S模糊系统的局部特性。首先，通过优化集合的方法研究了模糊系统的局部稳定及镇定，使所得结果不但能够得到更大的局部稳定区域而且应用范围更广；其次，针对不同种类的扰动，设计优化算法抑制其对系统的影响并探明扰动与不变集之间的关系；然后，根据前件变量已知和未知两种情况设计不同的观测器使得误差系统局部稳定，讨论误差系统的初始值与稳定区域的关系并给出了解决方法；进一步，通过定义新的向量泛数得到了模糊时滞系统的局部稳定区域。