New Optimal Approach for the Identification of Takagi-Sugeno Fuzzy Model

A novel optimal method is developed to improve the identification and estimation of Takagi-Sugeno (TS) fuzzy model. The idea comes from the fact that the main drawback of T-S model is that it can not be applied when the membership functions are overlapped by pairs. This limits the application of the T-S model because this type of membership function has been widely used in the stability and controller design of fuzzy systems. It is also very popular in industrial control applications. The method presented here can be considered as a generalized version of T-S fuzzy model with optimized performance in approximating nonlinear functions. Various examples are chosen to show the high function approximation accuracy and fast convergence obtained by applying the proposed method in approximating nonlinear systems locally and globally in comparison with the original T-S model

An Optimal T-S Model for the Estimation and Identification of Nonlinear Functions

A novel optimal method is developed to improve the identification and estimation of Takagi-Sugeno (TS) fuzzy model. The idea comes from the fact that the main drawback of T-S model is that it can not be applied when the membership functions are overlapped by pairs. This limits the application of the T-S model because this type of membership function has been widely used in the stability and controller design of fuzzy systems. It is also very popular in industrial control applications. The method presented here can be considered as a generalized version of T-S fuzzy model with optimized performance in approximating nonlinear functions. Various examples are chosen to show the high function approximation accuracy and fast convergence obtained by applying the proposed method in approximating nonlinear systems locally and globally in comparison with the original T-S model

A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters' weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm

Adaptación paramétrica de un sistema borroso mediante el filtro de Kalman extendido

Cuando se pretende analizar o controlar un sistema cuyo modelo se ha obtenido ´únicamente en base a datos de entrada/salida, es fundamental la precisión en el modelo. Por otro lado, para que el procedimiento sea practico, la etapa de modelado ha de ser eficiente computacionalmente hablando. En este sentido, se presenta en este trabajo la aplicación del filtro de Kalman extendido para la adaptación paramétrica de un modelo borros

Variable structure control with chattering reduction of a generalized T-S model

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) is presented. The main objective is to obtain an improved performance of highly non-linear unstable systems. New functions for chattering reduction and error convergence without sacrificing invariant properties are proposed. The main feature of the proposed method is that the switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules; together with the state variables. In this work, a tuning of the well known weighting parameters approach is proposed to optimize local and global approximation and modelling capability of the Takagi-Sugeno (T-S) fuzzy model to improve the choice of the performance index and minimize it. The main problem encountered is that the T-S identification method can not be applied when the membership functions are overlapped by pairs. This in turn restricts the application of the T-S method because this type of membership function has been widely used in control applications. The approach developed here can be considered as a generalized version of the T-S method. An inverted pendulum mounted on a cart is chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of the proposed estimation approach in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the estimation method and the robustness of the chattering reduction algorithm. In this paper, we prove that the proposed estimation algorithm converge the very fast, thereby making it very practical to use. The application of the proposed FLC-VSC shows that both alleviation of chattering and robust performance are achieved

Improvement of Takagi-Sugeno Fuzzy Model for the Estimation of Nonlinear Functions

Two new and efficient approaches are presented to improve the local and global estimation of the Takagi-Sugeno (T-S) fuzzy model. The main aim is to obtain high function approximation accuracy and fast convergence. The main problem is that the T-S identification method can not be applied when the membership functions are overlapped by pairs. The approaches developed here can be considered as generalized versions of T-S method with optimized performance. The first uses the minimum norm approach to search for an exact optimum solution at the expense of increasing complexity and computational cost. The second is a simple and less computational method, based on weighting of parameters. Illustrative examples are chosen to evaluate the potential, simplicity and remarkable performance of the proposed methods and the high accuracy obtained in comparison with the original T-S model

Asymptotically exact stabilisation for constrained discrete Takagi-Sugeno systems via set-invariance

[EN] Given a Takagi-Sugeno (TS) system, this paper proposes a novel methodology to obtain the state feedback controller guaranteeing, asymptotically as a Polya-related complexity parameter grows, the largest (membership-shape independent) possible domain-of-attraction with contraction-rate performance lambda, based on polyhedral lambda-contractive sets from constrained linear systems literature. The resulting controller is valid for any realisation of the memberships, as usual in most TS literature. For a finite complexity parameter, an inner estimate of such largest set is obtained; the frontier of such approximation can be understood as the level set of a polyhedral control-Lyapunov function. Convergence of a proposed iterative algorithm is asymptotically necessary and sufficient for TS system stabilisation: for a high-enough value of the complexity parameter, any conceivable shape-independent Lyapunov controller design procedure will yield a proven domain of attraction smaller or equal to the algorithm's output. (C) 2016 Elsevier B.V. All rights reserved.This work has been supported by grants DPI2015-70433- P and DPI2016-81002-R, from Spanish Government (MINECO) and grant PROMETEOII/2013/004 from Generalitat Valenciana.Ariño-Latorre, CV.; Sala, A.; Pérez Soler, E.; Bedate Boluda, F.; Querol-Ferrer, A. (2017). Asymptotically exact stabilisation for constrained discrete Takagi-Sugeno systems via set-invariance. Fuzzy Sets and Systems. 316:117-138. https://doi.org/10.1016/j.fss.2016.10.004S11713831

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use