区间二型T-S模型非线性系统非二次稳定性和广义耗散性分析以及控制与滤波

Compared with type-1 model, the interval type-2 T-S based nonlinear systems can represent and capture the uncertain knowledge and information contained in membership functions, while more difficulties appear in stability analysis and controller as well as filter design for this class of systems. Up to now, many of results reported are conservative since quadratic Lyapunov function does not use the information of type-2 basis functions. For this reason, it is necessary to develop some new approaches for improving these sufficient quadratic stability results. This project deals with some challenging problems such as nonquadratic stability , controller and filter design for interval type-2 T-S model based nonlinear systems. Among these are establishing nonquadratic stability conditions and generalized dissipativity performance, via type-2 basis function depedent Lyapunov function and new approach to deal with multi-type-2 fuzzy sum; developing effective algorithms of controller gains in terms of the nonquadratic stability condition based nonlinear matrix inequalities in state feedback or output feedback control problems; deriving existance conditions of filter and obtaining filtering algorithms via nonlinear transformation of nonlinear matrix inequalities related to the corresponding filtering error systems. Also, making use of the interval type-2 T-S modeling approach, these filtering algorithms may be used to deal with some real world systems such as tunnel diode circuit systems and robot control. This project will establish less conservative nonquadratic stability criteria and develop new controller and filter for interval type-2 T-S based nonlinear systems, and also is of potential practical values in real control engineering such as in electronic industry as well as in robot industry.

与一型系统相比，区间二型T-S模型能更好地处理隶属函数的不确定性，但分析与设计更复杂。由于未能利用二型基函数的信息，现有的研究结果具有较大的保守性。本项目将研究区间二型系统的非二次稳定性和控制与滤波问题。研究内容包括：构造依赖二型基函数的Lyapunov函数，提出新的方法处理多重二型模糊和和估计性能泛函，建立非二次稳定性和广义耗散性能准则；对状态和输出反馈等控制问题，基于闭环形式的非二次稳定性条件推出相关的非线性不等式，研究通过设计有效算法求解控制器增益的问题；对由非二次稳定性条件推出的滤波器参数矩阵满足的非线性矩阵不等式，研究如何构造非线性矩阵变换，建立滤波器存在的条件和求解算法问题。建立隧道二极管电路的区间二型T-S模型，对提出的理论结果仿真验证。项目的研究将建立保守性小的非二次稳定性条件并提出有效的控制和滤波方法，在机器人和电力电子产业等控制工程领域有潜在的应用价值。

本项目研究了区间二型(IT2)T-S模糊非线性系统的广义耗散性能分析以及控制器和滤波器设计问题。由于IT2模型推广和发展了一型模糊系统理论，从而对以往的结果进行了改进。非二次Lyapunov函数含有模糊基函数的信息，获得的条件具有较小的保守性。.主要研究成果包括：用依赖二型基函数的非二次Lyapunov函数，特别是线积分等数学工具，建立了系统满足渐近稳定和广义耗散性能的更一般性的充分条件；基于投影引理、Finsler引理，参数化方法，结合新的矩阵解耦技术，锥补偿线性化算法和二次规划等方法设计了控制器和滤波器，并将结果推广到带有网络诱导时滞和参数不确定的IT2网络系统中。通过四年的研究，本项目的研究目标已完成。主要研究成果已在系统与控制学术期刊上发表论文14篇，其中SCI收录期刊论文7篇，SCI在审5篇。本项目已培养博士生1名，培养研究生15名。