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1

Relaxed formulation of the design conditions for Takagi-Sugeno fuzzy virtual actuators

Filasova A., Krokavec D., Liscinsky P.

Archives of Control Sciences

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2016

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Vol. 26, no. 2

199--221

EN

The H∞ norm approach to virtual actuators design, intended to Takagi-Sugeno fuzzy continuous-time systems, is presented in the paper. Using the second Ljapunov method, the design conditions are formulated in terms of linear matrix inequalities in adapted bounded real lemma structures. Related to the static output controller, and for systems under influence of single actuator faults, the design steps are revealed for a three-tank system plant.

2

Nonlinear actuator fault estimation observer: an inverse system approach via a T-S fuzzy model

Xu D., Jiang B., Shi P.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 1

183-196

EN

Based on a Takagi-Sugeno (T-S) fuzzy model and an inverse system method, this paper deals with the problem of actuator fault estimation for a class of nonlinear dynamic systems. Two different estimation strategies are developed. Firstly, T-S fuzzy models are used to describe nonlinear dynamic systems with an actuator fault. Then, a robust sliding mode observer is designed based on a T-S fuzzy model, and an inverse system method is used to estimate the actuator fault. Next, the second fault estimation strategy is developed. Compared with some existing techniques, such as adaptive and sliding mode methods, the one presented in this paper is easier to be implemented in practice. Finally, two numerical examples are given to demonstrate the efficiency of the proposed techniques.

3

A novel fuzzy c-regression model algorithm using a new error measure and particle swarm optimization

Soltani M., Chaari A., Ben Hmida F.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 3

617-628

EN

This paper presents a new algorithm for fuzzy c-regression model clustering. The proposed methodology is based on adding a second regularization term in the objective function of a Fuzzy C-Regression Model (FCRM) clustering algorithm in order to take into account noisy data. In addition, a new error measure is used in the objective function of the FCRM algorithm, replacing the one used in this type of algorithm. Then, particle swarm optimization is employed to finally tune parameters of the obtained fuzzy model. The orthogonal least squares method is used to identify the unknown parameters of the local linear model. Finally, validation results of two examples are given to demonstrate the effectiveness and practicality of the proposed algorithm.

4

On choosing the fuzziness parameter for identifying TS models with multidimensional membership functions

Kroll A.

Journal of Artificial Intelligence and Soft Computing Research

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2011

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Vol. 1, No. 4

283--300

EN

Fuzzy clustering is a well-established method for identifying the structure/fuzzy partitioning of Takagi-Sugeno (TS) fuzzy models. The clustering algorithms require choosing the fuzziness parameter m. Prior work in the area of pattern recognition shows, that a suitable choice of m is application- dependent. Yet, the default of m=2 is commonly chosen. This paper examines the suitable choice of m for identifying TS models. The focus is on models that use the classifiers resulting from fuzzy clustering as multi-dimensional membership functions or their projection and approximation. At first, the differentiability and grouping properties of the fuzzy classifiers are analyzed to make a general recommendation of choosing m(1;3). Besides, the effect of the cluster number c on the classification fuzziness is examined. Finally, requirements that are specific to TS modeling are introduced, which narrow down the suitable range for m. Building on algorithm analysis and four case studies (function approximation, a vehicle engine and an axial compressor application for nonlinear regression), it is demonstrated that choosing m2(1;1.3) for local and m2(1;1.5) for global estimation will typically provide for good results.

5

Comparision of Two Construction Algorithms for Takagi-Sugeno Fuzzy Models

Nelles O., Fink A., Babuska R., Setnes M.

International Journal of Applied Mathematics and Computer Science

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2000

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Vol. 10, no 4

835-855

EN

This paper compares two different approaches to the construction of Takagi-Sugeno fuzzy models from data. These models approximate nonlinear systems by means of interpolation between local linear models. The main issue in the construction of Takagi-Sugeno models is the decomposition of the operating space into validity regions for the local models. The way this decomposition is done influences the complexity, accuracy and transparency of the obtained model. The first of the presented methods, the local linear model tree (LOLIMOT) algorithm generates incrementally the fuzzy model by axis-orthogonal decomposition of the input space. In the other method, product-space fuzzy clustering (the Gustafson-Kessel algorithm) is used to partition the available data into fuzzy subsets. The fundamental advantages and drawbacks of both the alternative strategies are pointed out. Their properties and real-world applicability are illustrated by building a dynamic model of a truck Diesel engine turbocharger.