多变量模糊系统理论及应用研究

Modeling, analysis and control of multivariable fuzzy system, an important direction of intelligent techniques, are to analyze and deal with complex MIMO dynamic systems. A complex multivariable system features nonlinearity, uncertainty, multiple variables and couple action. It is difficult or even impossible to effectively deal with this kind of system with the existing conventional system and control theories based on classical logic. The theory of fuzzy sets and fuzzy systems open a new alternative way to modeling, analysis and control of such systems. But most developments are limited during the dealing with SISO systems in recent years. Therefore, the study on multivariable fuzzy system is of significance in respects of theory and application, and becomes one of the focuses on the research of the fuzzy logic techniques. In this dissertation, several conclusions about the multivariable fuzzy system theory have been achieved. The whole thesis includes two parts, and the main contents and conclusions are summarized as follows: In the first part, the theory about modeling, analysis and control of multivariable fuzzy systems is studied, including 1 The study on generalized fuzzy basis function based multivariable fuzzy system model By analyzing the existing modeling methods of multivariable fuzzy systems, enlightened by the fuzzy cell to cell mapping model proposed by L.M.Jia, a new analytical description of the MIMO fuzzy rules generalized fuzzy basis function (GFBF) is put forwards under the deterministic definition of the fuzzy cellization. It cannot only simultaneously the numerical data and linguistic knowledge of the complex systems, but also contains many kinds of fuzzy basis function according to the basic properties of GFBF. Consequently, generalized fuzzy basis function series (GFBFS), an efficient and concise modeling method for MIMO fuzzy systems, is proposed through the reasonable selection for the decision making logic used in the fuzzy inference mechanism, which can be proved to approximate arbitrary nonlinear functions to any degree of accuracy. Based on this model, an identification algorithm utilizing numerical data is provided and its convergence property is detailed studied. Furthermore, in order to improve the computational efficiency of the identification algorithm, a fast technique based on ρ cut equivalent system is put forward. The simulation results about typical system and practical industrial plant demonstrate its effectiveness. 2 The study on analysis of the dynamic properties of the MIMO fuzzy systems By reviewing the existing analyzing method of fuzzy systems, and based on the idea that the dynamics of any complex system is the aggregation of its implicit stable sub dynamics and unstable sub dynamics, system decomposition method is proposed to make the system properties easier to be recognized. Furthermore, the filtering operation is used to reasonable eliminate the less significant factors and make the dominant dynamics emerge. Then, the system behavior can be evaluated directly from the α cut equivalent system structure characterized by the cell to cell mapping. This provides a new approach to analyze the asymptotic response of the complex dynamic system. 3 The study on fuzzy sliding-mode based self learning multivariable fuzzy controller (FSM MFC) After a brief introduction to the state of arts of the researches on multivariable fuzzy controller (MFC), the limitation of indirect MFC based on the controlled system model is summarized. More and more researchers concentrate on the study of direct MFC and the general purposed model free MFC becomes the focus on the researches on fuzzy logic control theory and its application. Based on the method of sliding mode variable structure control (VSC) dealing with SISO and n the order systems, the concept of fuzzy sliding mode (FSM) is defined in the state space, and the performance of the closed loop system is significantly improved through the introduction to another control input. Meantime, by