T-S模糊非线性系统的几个控制理论问题研究

Although it makes great progress on researching T-S fuzzy nonlinear systems, there are few results of controllability in terms of Lie algebra due to its difficulties. And all results reported up to now are sufficient but not necessary due to nonlinearity of this class of systems. For this reason, it is necessary to develop some new approaches for improving these sufficient results. This project deals with some challenging problems of T-S model based on nonlinear systems. Among these are characterizing controllability in terms of Lie algebra which is based on existence of the largest integral sub-manifold; establishing stability conditions with less conservativeness combining fuzzy Lyapunov functions (of convex combination, of homogeneous polynomial and of line integral types) with the tensor product technique for handling the multi-convex combination matrix inequality of fuzzy sum; developing control and filtering algorithms via quadratic programming with the help of the technique for transforming closed-loop conditions in view of some new equivalent relation for decoupling matrices as well as the more general closed-loop conditions proposed. If possible, these analysis and synthesis approaches proposed can be extended to muti-dimensional discrete T-S fuzzy nonlinear systems. Also, making use of the T-S modeling approach, these control and filtering algorithms may be used to deal with some real world systems such as tunnel diode circuit systems, chaotic Lorenz systems as well as multi-scale control and filtering problems for some classes of cooperation targets in space. This project will complete and develop the theory of T-S fuzzy nonlinear systems, and also is of potential practical values in real control engineering such as in electronic industry as well as in aeronautics and space industry.

T-S模糊非线性系统研究虽取得了重要进展，由于难度大用李代数研究其可控性仅有极少结果，因其非线性特性，现有结果都是充分而非必要的，需要寻求新方法改进这些结果。本项目将研究这一方向中几个重要且具有一定难度的问题。内容包括利用李代数方法基于状态空间最大积分子流型的存在性建立用可达李代数表征的系统可控性条件；用模糊Lyapunov 函数（多重凸组合、齐次多项式、线积分型）与关于模糊和的多重凸组合矩阵不等式张量积处理技术相结合方法建立更具一般性的稳定性条件；基于新的保守性小的闭环条件，结合关于解耦矩阵的等价关系变换闭环条件技术，用二次规划方法设计控制和滤波算法；将得到结果推广到多维T-S模糊非线性系统；并应用T-S模型方法研究隧道二极管电路、洛伦兹混沌系统及几类空间合作目标多尺度控制和滤波问题。项目成果将完善和发展T-S模糊系统理论，在实际控制工程特别是电力电子产业和航空航天等领域有潜在应用价值。

本项目研究了T-S模型非线性系统的稳定性分析以及控制器和滤波器设计问题，由于其非线性的特性，现有结果都是充分而非必要的。基于新的思路和新型的数学工具，研究了这一方向中几个重要且具有一定难度的问题，从而对以往的结果进行了改进。主要内容包括；用模糊Lyapunov函数（多重凸组合、线积分型）与关于模糊和的多重凸组合的矩阵不等式张量积相结合的方法建立更具一般性的稳定性条件；基于新的保守性小的闭环条件，结合关于解耦矩阵的等价关系变换闭环条件技术，用二次规划方法设计控制和滤波算法；将结果推广到多维T-S模糊非线性系统。通过四年的研究，本项目的研究目标已基本达到。主要研究成果已在系统与控制学术期刊和学术会议上发表论文24篇，其中SCI收录期刊论文5篇，SCI在审4篇，EI收录论文9篇。本项目已培养研青年教师2名，毕业研究生20名，在读6名。