The composition of simple local models for approximating complex nonlinear mappings is a common practice in recent modeling and control literature. This paper presents a comparative analysis of two different local approaches: the neuro-fuzzy inference system and the lazy learning approach. Neuro-fuzzy is a hybrid representation which combines the linguistic description typical of fuzzy inference systems, with learning procedures inspired by neural networks. Lazy learning is a memory-based technique that uses a query-based approach to select the best local model configuration by assessing and comparing different alternatives in cross-validation. In this paper, the two approaches are compared both as learning algorithms, and as identification modules of an adaptive control system. We show that lazy learning is able to provide better modeling accuracy and higher control performance at the cost of a reduced readability of the resulting approximator. Illustrative examples of identi cation and control of a nonlinear system starting from simulated data are given.

A number of techniques have been introduced to construct fuzzy models from measured data. Most attention has been focused on multiple-input, single-output (MISO) systems. This article concentrates on the identification of multiple-input, multiple-output (MIMO) systems by means of product-space fuzzy clustering with adaptive distance measure (the Gustafson-Kessel algorithm). The MIMO model is represented as a set of coupled input-output MISO models of the Takagi-Sugeno type. Knowledge of the physical structure can easily be incorporated in the structure of the model. Software implementation in the form of a Matlab toolbox is briefly described. A simulation example of four cascaded tanks is given.

: A competitive exception learning algorithm for finding a non-linear mapping is proposed which puts the emphasis on the discovery of the important exceptions rather than the main rules. Todoso,wefirstclustertheoutputspace using a competitive fuzzy clustering algorithm and derive a fuzzy frequency distribution describing the general, average system's output behavior. Next, welook for a fuzzy partitioning of the input space in suchaway that the corresponding fuzzy output frequency distributions `deviate at most' from the average one as found in the first step. In this way, the most important `exceptional regions' in the input-output relation are determined. Using the joint input-output fuzzy frequency distributions, the complete input-output function as extracted from the data, can be expressed mathematically. In addition, the exceptions encountered can be collected and described as a set of fuzzy if-then-else-rules. Besides presenting a theoretical description of the new exception le...

A competitive exception learning algorithm for finding a non-linear mapping is proposed which puts the emphasis on the discovery of the important exceptions rather than the main rules. To do so,we first cluster the output space using a competitive fuzzy clustering algorithm and derive a fuzzy frequency distribution describing the general, average system's output behavior. Next, we look for a fuzzy partitioning of the input space in such away that the corresponding fuzzy output frequency distributions deviate at most' from the average one as found in the first step. In this way, the most important exceptional regions' in the input-output relation are determined. Using the joint input-output fuzzy frequency distributions, the complete input-output function as extracted from the data, can be expressed mathematically. In addition, the exceptions encountered can be collected and described as a set of fuzzy if-then-else-rules. Besides presenting a theoretical description of the new...

The generation of the sequence of control inputs along a given state trajectory for a nonlinear system is described. A nonlinear system is linearized at predefined points in the product space of the states and control inputs and then approximated by local linear fuzzy models. Based on this approximation the system is controlled by a set of local linear Takagi-Sugeno fuzzy controllers. The local control laws designed for the error system incorporate both the desired and the actual state as well as the corresponding control input. Normally, the desired state is defined by the user but the related control input cannot always be calculated in a unique way especially for a non-square system. The proposed method generates the desired control inputs on the basis of the states and its derivatives using inverse fuzzy models of the system. In an optimization loop the control inputs are corrected by the analytical forward model of the nonlinear system. Keywords Takagi Sugeno fuzzy systems, fuzzy...

In this paper a global linearization of fuzzy model is given. The parameters of global linear model are obtained by instantaneous linearization of fuzzy model. The model is given in the form of the Sugeno-Takagi fuzzy model.