Fuzzy Model Identification for Control, 2003

Overview Since the early 1990s, fuzzy modeling and identification from process data have been and continue to be an evolving subject of interest. Although the application of fuzzy models proved to be effective for the approxima­ tion of uncertain nonlinear processes, the data-driven identification offuzzy models alone sometimes yields complex and unrealistic models. Typically, this is due to the over-parameterization of the model and insufficient in­ formation content of the identification data set. These difficulties stem from a lack of initial a priori knowledge or information about the system to be modeled. To solve the problem of limited knowledge, in the area of modeling and identification, there is a tendency to blend information of different natures to employ as much knowledge for model building as possible. Hence, the incorporation of different types of a priori knowledge into the data-driven fuzzy model generation is a challenging and important task. Motivated by our research into this topic, our book presents new ap­ proaches to the construction of fuzzy models for model-based control. New model structures and identification algorithms are described for the effec­ tive use of heterogenous information in the form of numerical data, qualita­ tive knowledge and first-principle models. By exploiting the mathematical properties of the proposed model structures, such as invertibility and local linearity, new control algorithms will be presented.

1 Introduction.- 1.1 Fuzzy Modeling with the Use of Prior Knowledge.- 1.2 Fuzzy model-based Control.- 1.3 Illustrative Examples.- 1.4 Summary.- 2 Fuzzy Model Structures and their Analysis.- 2.1 Introduction to Fuzzy Modeling.- 2.2 Takagi-Sugeno Fuzzy Models (TS).- 2.3 Fuzzy Models with Multivariate Membership Functions (MMF).- 2.4 Input Reduction of Fuzzy Models.- 2.5 Fuzzy Model Inversion.- 2.6 Linearization and Derivatives of Fuzzy Models.- 3 Fuzzy Models of Dynamical Systems.- 3.1 Data-Driven Empirical Modeling.- 3.2 TS Fuzzy Models of Dynamical Systems.- 3.3 TS Fuzzy Models of MIMO Systems.- 3.4 Hybrid Fuzzy Convolution Model (HFCM).- 3.5 Fuzzy Hammerstein Model (FH).- 4 Fuzzy Model Identification.- 4.1 Identification as an Optimization Problem.- 4.2 Consequent Parameter Identification.- 4.3 Model Structure Identification.- 4.4 Antecedent Membership Function Identification.- 4.5 MMF Fuzzy Model Identification.- 4.6 Hybrid Fuzzy Convolution Model Identification.- 4.7 Fuzzy Hammerstein Model Identification.- 5 Fuzzy Model based Control.- 5.1 Introduction to Fuzzy Control.- 5.2 Inverse Fuzzy Model based (Adaptive) Control.- 5.3 Introduction to Model Predictive Control.- 5.4 TS Fuzzy Model based Predictive Control.- 5.5 MIMO Fuzzy model based Predictive Control.- 5.6 HFCM based Predictor Corrector Controller.- 5.7 HFCM based Predictive Control.- 5.8 Fuzzy Hammerstein Model based Predictive Control.- 5.9 Grey-Box TS Fuzzy Model based Adaptive Control.- A Process Models Used for Case Studies.- A.l Model of the pH Process.- A.2 Electrical Water-Heater.- A.3 Distillation Column.- A.4 Model of the liquid level rig.- References.