New Approach on Robust Delay-Dependent H∞ Control for Uncertain T-S Fuzzy Systems With Interval Time-Varying Delay

This paper investigates the robust H∞ control for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, delay-dependent stability criteria are derived for the control problem. Because neither any model transformation nor free weighting matrices are employed in our theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions. Also, the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

Robust fuzzy Gustafson-Kessel clustering for nonlinear system identification

This paper deals with Takagi-Sugeno (TS) fuzzy model identification of nonlinear systems using fuzzy clustering. In particular, an extended fuzzy Gustafson-Kessel (EGK) clustering algorithm, using robust competitive agglomeration (RCA), is developed for automatically constructing a TS fuzzy model from system input-output data. The EGK algorithm can automatically determine the 'optimal' number of clusters from the training data set. It is shown that the EGK approach is relatively insensitive to initialization and is less susceptible to local minima, a benefit derived from its agglomerate property. This issue is often overlooked in the current literature on nonlinear identification using conventional fuzzy clustering. Furthermore, the robust statistical concepts underlying the EGK algorithm help to alleviate the difficulty of cluster identification in the construction of a TS fuzzy model from noisy training data. A new hybrid identification strategy is then formulated, which combines the EGK algorithm with a locally weighted, least-squares method for the estimation of local sub-model parameters. The efficacy of this new approach is demonstrated through function approximation examples and also by application to the identification of an automatic voltage regulation (AVR) loop for a simulated 3 kVA laboratory micro-machine system.

A New Gradient Descent Approach for Local Learning of Fuzzy Neural Models

The majority of reported learning methods for Takagi-Sugeno-Kang fuzzy neural models to date mainly focus on the improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behaviour when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, to identify the corresponding consequent models which can be directly explained in terms of system behaviour presents a critical step in fuzzy neural modelling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practised in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. A new Jacobian matrix is thus proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues about the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.

Lógica Fuzzy para Controle de pH em um Processo Petrolífero

This work proposes the design, the performance evaluation and a methodology for tuning the initial MFs parameters of output of a function based Takagi-Sugeno-Kang Fuzzy-PI controller to neutralize the pH in a stirred-tank reactor. The controller is designed to perform pH neutralization of industrial plants, mainly in units found in oil refineries where it is strongly required to mitigate uncertainties and nonlinearities. In addition, it adjusts the changes in pH regulating process, avoiding or reducing the need for retuning to maintain the desired performance. Based on the Hammerstein model, the system emulates a real plant that fits the changes in pH neutralization process of avoiding or reducing the need to retune. The controller performance is evaluated by overshoots, stabilization times, indices Integral of the Absolute Error (IAE) and Integral of the Absolute Value of the Error-weighted Time (ITAE), and using a metric developed by that takes into account both the error information and the control signal. The Fuzzy-PI controller is compared with PI and gain schedule PI controllers previously used in the testing plant, whose results can be found in the literature.

Desenvolvimento de um ambiente para projeto de controladores fuzzy para dispositivos móveis

Fuzzy intelligent systems are present in a variety of equipment ranging from household appliances to Fuzzy intelligent systems are present in a variety of equipment ranging from household appliances to small devices such as digital cameras and cell phones being used primarily for dealing with the uncertainties in the modeling of real systems. However, commercial implementations of Fuzzy systems are not general purpose and do not have portability to different hardware platforms. Thinking about these issues this work presents the implementation of an open source development environment that consists of a desktop system capable of generate Graphically a general purpose Fuzzy controller and export these parameters for an embedded system with a Fuzzy controller written in Java Platform Micro Edition To (J2ME), whose modular design makes it portable to any mobile device that supports J2ME. Thus, the proposed development platform is capable of generating all the parameters of a Fuzzy controller and export it in XML file, and the code responsible for the control logic that is embedded in the mobile device is able to read this file and start the controller. All the parameters of a Fuzzy controller are configurable using the desktop system, since the membership functions and rule base, even the universe of discourse of the linguistic terms of output variables. This system generates Fuzzy controllers for the interpolation model of Takagi-Sugeno. As the validation process and testing of the proposed solution the Fuzzy controller was embedded on the mobile device Sun SPOT ® and used to control a plant-level Quanser®, and to compare the Fuzzy controller generated by the system with other types of controllers was implemented and embedded in sun spot a PID controller to control the same level plant of Quanser®

Design of fuzzy regulators with optimal initial conditions compensation

In almost all cases, the goal of the design of automatic control systems is to obtain the parameters of the controllers, which are described by differential equations. In general, the controller is artificially built and it is possible to update its initial conditions. In the design of optimal quadratic regulators, the initial conditions of the controller can be changed in an optimal way and they can improve the performance of the controlled system. Following this idea, a LNU-based design procedure to update the initial conditions of PI controllers, considering the nonlinear plant described by Takagi-Sugeno fuzzy models, is presented. The importance of the proposed method is that it also allows other specifications, such as, the decay rate and constraints on control input and output. The application in the control of an inverted pendulum illustrates the effectively of proposed method.

Tuning of fuzzy inference systems through unconstrained optimization techniques

This paper presents a new methodology for the adjustment of fuzzy inference systems. A novel approach, which uses unconstrained optimization techniques, is developed in order to adjust the free parameters of the fuzzy inference system, such as its intrinsic parameters of the membership function and the weights of the inference rules. This methodology is interesting, not only for the results presented and obtained through computer simulations, but also for its generality concerning to the kind of fuzzy inference system used. Therefore, this methodology is expandable either to the Mandani architecture or also to that suggested by Takagi-Sugeno. The validation of the presented methodology is accomplished through an estimation of time series. More specifically, the Mackey-Glass chaotic time series estimation is used for the validation of the proposed methodology.

A comparative study between two relaxed LMI-based fuzzy control designs

A comparative study, with theoretical analysis and digital simulations, of two conditions based on LMI for the quadratic stability of nonlinear continuous-time dynamic systems, described by Takagi-Sugeno fuzzy models, are presented. This paper shows that the methods proposed by Teixeira et. al. in 2003 provide better or at least the same results of a recent method presented in the literature. © 2005 IEEE.

Efficient parametric adjustment of fuzzy inference system using unconstrained optimization

This paper presents a new methodology for the adjustment of fuzzy inference systems, which uses technique based on error back-propagation method. The free parameters of the fuzzy inference system, such as its intrinsic parameters of the membership function and the weights of the inference rules, are automatically adjusted. This methodology is interesting, not only for the results presented and obtained through computer simulations, but also for its generality concerning to the kind of fuzzy inference system used. Therefore, this methodology is expandable either to the Mandani architecture or also to that suggested by Takagi-Sugeno. The validation of the presented methodology is accomplished through estimation of time series and by a mathematical modeling problem. More specifically, the Mackey-Glass chaotic time series is used for the validation of the proposed methodology. © Springer-Verlag Berlin Heidelberg 2007.

Estabilização de sistemas fuzzy T-S incertos usando realimenta̧ão derivativa

In some practical problems, for instance, in the suppression of vibration in mechanical systems, the state-derivative signals are easier to obtain than the state signals. Thus, a method for state-derivative feedback design applied to uncertain nonlinear systems is proposed in this work. The nonlinear systems are represented by Takagi-Sugeno fuzzy models during the modeling of the problem, allowing to use Linear Matrix Inequalities (LMIs) in the controller design. This type of modeling ease the control design, because, LMIs are easily solved using convex programming technicals. The control design aimed at system stabilisation, with or without bounds on decay rate. The efficiency of design procedure is illustrated through a numerical example.

Improving the stability conditions of TS fuzzy systems with fuzzy Lyapunov functions

In this paper, the fuzzy Lyapunov function approach is considered for stabilizing continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing a slack LMI variable into the problem formulation. The stability results are thus used in the state feedback design which is also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilizing conditions presented. © 2011 IFAC.

Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions

In this article, the fuzzy Lyapunov function approach is considered for stabilising continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing slack LMI variables into the problem formulation. The relaxation conditions given can also be used with a class of fuzzy Lyapunov functions which also depends on the membership function first-order time-derivative. The stability results are thus extended to systems with large number of rules under membership function order relations and used to design parallel-distributed compensation (PDC) fuzzy controllers which are also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilising conditions presented. © 2013 Copyright Taylor and Francis Group, LLC.

Robust Switched Control Design for Nonlinear Systems Using Fuzzy Models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estimación de modelos borrosos y su aplicación al control óptimo

El objetivo de la presentación es dar a conocer los últimos trabajos del Grupo de Investigación sobre últimos trabajos del Grupo de Investigación sobre Control Borroso. • Obtención de modelos precisos de sistemas no lineales basados en sistemas borrosos – Mamdani – Takagi-Sugeno – Linealización • Generalización del método propuesto por T-S • Identificación iterativa basada en el Filtro de Kalman • Sistemas de control basados en el modelo TS obtenido – LQR

Off-line signature verification and forgery detection using fuzzy modeling

Automatic signature verification is a well-established and an active area of research with numerous applications such as bank check verification, ATM access, etc. This paper proposes a novel approach to the problem of automatic off-line signature verification and forgery detection. The proposed approach is based on fuzzy modeling that employs the Takagi-Sugeno (TS) model. Signature verification and forgery detection are carried out using angle features extracted from box approach. Each feature corresponds to a fuzzy set. The features are fuzzified by an exponential membership function involved in the TS model, which is modified to include structural parameters. The structural parameters are devised to take account of possible variations due to handwriting styles and to reflect moods. The membership functions constitute weights in the TS model. The optimization of the output of the TS model with respect to the structural parameters yields the solution for the parameters. We have also derived two TS models by considering a rule for each input feature in the first formulation (Multiple rules) and by considering a single rule for all input features in the second formulation. In this work, we have found that TS model with multiple rules is better than TS model with single rule for detecting three types of forgeries; random, skilled and unskilled from a large database of sample signatures in addition to verifying genuine signatures. We have also devised three approaches, viz., an innovative approach and two intuitive approaches using the TS model with multiple rules for improved performance. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.