Robert Babuska

Fuzzy Modeling for Control

From the Publisher: Fuzzy Modeling for Control addresses fuzzy modeling from the systems and control engineering point of view. It focuses on the selection of appropriate model structures, on the acquisition of dynamic fuzzy models from process measurements (fuzzy identification), and on the design of nonlinear controllers based on fuzzy models. The main features of the presented techniques are illustrated by means of simple examples. In addition, three real-world applications are described. Finally, software tools for building fuzzy models from measurements are available from the author.

Similarity measures in fuzzy rule base simplification

In fuzzy rule-based models acquired from numerical data, redundancy may be present in the form of similar fuzzy sets that represent compatible concepts. This results in an unnecessarily complex and less transparent linguistic description of the system. By using a measure of similarity, a rule base simplification method is proposed that reduces the number of fuzzy sets in the model. Similar fuzzy sets are merged to create a common fuzzy set to replace them in the rule base. If the redundancy in the model is high, merging similar fuzzy sets might result in equal rules that also can be merged, thereby reducing the number of rules as well. The simplified rule base is computationally more efficient and linguistically more tractable. The approach has been successfully applied to fuzzy models of real world systems.

Perspectives of fuzzy systems and control

Although fuzzy control was initially introduced as a model-free control design method based on the knowledge of a human operator, current research is almost exclusively devoted to model-based fuzzy control methods that can guarantee stability and robustness of the closed-loop system. State-of-the-art techniques for identifying fuzzy models and designing model-based controllers are reviewed in this article. Attention is also paid to the role of fuzzy systems in higher levels of the control hierarchy, such as expert control, supervision and diagnostic systems. Open issues are highlighted and an attempt is made to give some directions for future research.

Rule-based modeling: precision and transparency

This article is a reaction to recent publications on rule-based modeling using fuzzy set theory and fuzzy logic. The interest in fuzzy systems has recently shifted from the seminal ideas about complexity reduction toward data-driven construction of fuzzy systems. Many algorithms have been introduced that aim at numerical approximation of functions by rules, but pay little attention to the interpretability of the resulting rule base. We show that fuzzy rule-based models acquired from measurements can be both accurate and transparent by using a low number of rules. The rules are generated by product-space clustering and describe the system in terms of the characteristic local behavior of the system in regions identified by the clustering algorithm. The fuzzy transition between rules makes it possible to achieve precision along with a good qualitative description in linguistic terms. The latter is useful for expert evaluation, rule-base maintenance, operator training, control systems design, user interfacing, etc. We demonstrate the approach on a modeling problem from a recently published article.

Modified Gath-Geva fuzzy clustering for identification of Takagi-Sugeno fuzzy models

The construction of interpretable Takagi-Sugeno (TS) fuzzy models by means of clustering is addressed. First, it is shown how the antecedent fuzzy sets and the corresponding consequent parameters of the TS model can be derived from clusters obtained by the Gath-Geva (GG) algorithm. To preserve the partitioning of the antecedent space, linearly transformed input variables can be used in the model. This may, however, complicate the interpretation of the rules. To form an easily interpretable model that does not use the transformed input variables, a new clustering algorithm is proposed, based on the expectation-maximization (EM) identification of Gaussian mixture models. This new technique is applied to two well-known benchmark problems: the MPG (miles per gallon) prediction and a simulated second-order nonlinear process. The obtained results are compared with results from the literature.

An overview of fuzzy modeling for control

Abstract In this article some aspects of fuzzy modeling are discussed in connection with nonlinear system identification and control design. Methods for constructing fuzzy models from process data are reviewed, and attention is paid to the choice of a suitable fuzzy model structure for the identification task. Some approaches to control design based on a fuzzy model are outlined.

Fuzzy model for the prediction of unconfined compressive strength of rock samples

A data driven approach to the modeling of unconfined compressive strength of rock samples is presented. Fuzzy logic approach is used to represent a nonlinear relationship as a smooth concatenation of local linear submodels. The partitioning of the input space into fuzzy regions, represented by the individual rules, is obtained through fuzzy clustering. The numerical results are compared with a conventional statistical (multi-linear) model. It is shown that the fuzzy model is not only more accurate but as opposed to other black-box approaches (such as neural networks), it also provides some insight into the nonlinear relationship represented by the model.

Neuro-fuzzy methods for nonlinear system identification

Most processes in industry are characterized by nonlinear and time-varying behavior. Nonlinear system identification is becoming an important tool which can be used to improve control performance and achieve robust fault-tolerant behavior. Among the different nonlinear identification techniques, methods based on neuro-fuzzy models are gradually becoming established not only in the academia but also in industrial applications. Neuro-fuzzy modeling can be regarded as a gray-box technique on the boundary between neural networks and qualitative fuzzy models. The tools for building neuro-fuzzy models are based on combinations of algorithms from the fields of neural networks, pattern recognition and regression analysis. In this paper, an overview of neuro-fuzzy modeling methods for nonlinear system identification is given, with an emphasis on the tradeoff between accuracy and interpretability.

Fuzzy predictive control applied to an air-conditioning system

Abstract A method of designing a nonlinear predictive controller based on a fuzzy model of the process is presented. The Takagi-Sugeno fuzzy model is used as a powerful structure for representing nonlinear dynamic systems. An identification technique which enables the acquisition of the fuzzy model from process measurements is described. The fuzzy model is incorporated as a predictor in a nonlinear model-based predictive controller, using the internal model control scheme to compensate for disturbances and modeling errors. Since the model is nonlinear, a non-convex optimization problem must be solved at each sampling period. An optimization approach is proposed, that alleviates the computational burden of iterative optimization techniques, by using a combination of a branch-and-bound search technique, applied in a discretized space of the control variable, with an inverted fuzzy model of the process. The algorithm is applied to temperature control in air-conditioning system. Comparisons with a nonlinear predictive control scheme based on iterative numerical optimization show that the proposed method requires fewer computations and achieves better performance. Real-time control results are presented.

Multiobjective identification of Takagi-Sugeno fuzzy models

The problem of identifying the parameters of the constituent local linear models of Takagi-Sugeno fuzzy models is considered. In order to address the tradeoff between global model accuracy and interpretability of the local models as linearizations of a nonlinear system, two multiobjective identification algorithms are studied. Particular attention is paid to the analysis of conflicts between objectives, and we show that such information can be easily computed from the solution of the multiobjective optimization. This information is useful to diagnose the model and tune the weighting/priorities of the multiobjective optimization. Moreover, the result of the conflict analysis can be used as a constructive tool to modify the fuzzy model structure (including membership functions) in order to meet the multiple objectives. Simple illustrative examples as well as experimental results show the usefulness of the method.