On Switched Regulator Design of Uncertain Nonlinear Systems Using Takagi-Sugeno Fuzzy Models

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

Sistema baseado em regras fuzzy do tipo Takagi-Sugeno aplicado a ecos de radares meteorológicos

Pós-graduação em Ciências Ambientais - Sorocaba

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.

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.

Hardware/firmware implementation of a soft sensor using an improved version of a fuzzy identification algorithm

This paper presents the design and implementation of an embedded soft sensor, i. e., a generic and autonomous hardware module, which can be applied to many complex plants, wherein a certain variable cannot be directly measured. It is implemented based on a fuzzy identification algorithm called ""Limited Rules"", employed to model continuous nonlinear processes. The fuzzy model has a Takagi-Sugeno-Kang structure and the premise parameters are defined based on the Fuzzy C-Means (FCM) clustering algorithm. The firmware contains the soft sensor and it runs online, estimating the target variable from other available variables. Tests have been performed using a simulated pH neutralization plant. The results of the embedded soft sensor have been considered satisfactory. A complete embedded inferential control system is also presented, including a soft sensor and a PID controller. (c) 2007, ISA. Published by Elsevier Ltd. All rights reserved.

A Bayesian approach to fuzzy hypotheses testing for the estimation of optimal age for vaccination against measles

Fuzzy Bayesian tests were performed to evaluate whether the mother`s seroprevalence and children`s seroconversion to measles vaccine could be considered as ""high"" or ""low"". The results of the tests were aggregated into a fuzzy rule-based model structure, which would allow an expert to influence the model results. The linguistic model was developed considering four input variables. As the model output, we obtain the recommended age-specific vaccine coverage. The inputs of the fuzzy rules are fuzzy sets and the outputs are constant functions, performing the simplest Takagi-Sugeno-Kang model. This fuzzy approach is compared to a classical one, where the classical Bayes test was performed. Although the fuzzy and classical performances were similar, the fuzzy approach was more detailed and revealed important differences. In addition to taking into account subjective information in the form of fuzzy hypotheses it can be intuitively grasped by the decision maker. Finally, we show that the Bayesian test of fuzzy hypotheses is an interesting approach from the theoretical point of view, in the sense that it combines two complementary areas of investigation, normally seen as competitive. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

Controlo e optimização de sistemas AVAC recorrendo a técnicas de inteligência artificial

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Mecânica

Modeling of hybrid systems by piecewise decomposition

Piecewise linear models systems arise as mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous or discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phase portrait in different regions where each subregion is modeled as a two-dimensional linear time invariant system. Then the Takagi-Sugeno model, which is a combination of local model is calculated. The simulation results show that the Alpha partition is well-suited for dealing with such a system

“Reconstruction of Gene Regulatory Network from Expression Profile of Plasma RNA Data of Colorectal Cancer Patients using Soft Computing Techniques”

Microarray data analysis is one of data mining tool which is used to extract meaningful information hidden in biological data. One of the major focuses on microarray data analysis is the reconstruction of gene regulatory network that may be used to provide a broader understanding on the functioning of complex cellular systems. Since cancer is a genetic disease arising from the abnormal gene function, the identification of cancerous genes and the regulatory pathways they control will provide a better platform for understanding the tumor formation and development. The major focus of this thesis is to understand the regulation of genes responsible for the development of cancer, particularly colorectal cancer by analyzing the microarray expression data. In this thesis, four computational algorithms namely fuzzy logic algorithm, modified genetic algorithm, dynamic neural fuzzy network and Takagi Sugeno Kang-type recurrent neural fuzzy network are used to extract cancer specific gene regulatory network from plasma RNA dataset of colorectal cancer patients. Plasma RNA is highly attractive for cancer analysis since it requires a collection of small amount of blood and it can be obtained at any time in repetitive fashion allowing the analysis of disease progression and treatment response.

Klassifikationsgestützte on-line Adaption eines robusten beobachterbasierten Fehlerdiagnoseansatzes für nichtlineare Systeme

Diese Arbeit behandelt die Problemstellung der modellbasierten Fehlerdiagnose für Lipschitz-stetige nichtlineare Systeme mit Unsicherheiten. Es wird eine neue adaptive Fehlerdiagnosemethode vorgestellt. Erkenntnisse und Verfahren aus dem Bereich der Takagi-Sugeno (TS) Fuzzy-Modellbildung und des Beobachterentwurfs sowie der Sliding-Mode (SM) Theorie werden genutzt, um einen neuartigen robusten und nichtlinearen TS-SM-Beobachter zu entwickeln. Durch diese Zusammenführung lassen sich die jeweiligen Vorteile beider Ansätze miteinander kombinieren. Bedingungen zur Konvergenz des Beobachters werden als lineare Matrizenungleichungen (LMIs) abgeleitet. Diese Bedingungen garantieren zum einen die Stabilität und liefern zum anderen ein direktes Entwurfsverfahren für den Beobachter. Der Beobachterentwurf wird für die Fälle messbarer und nicht messbarer Prämissenvariablen angegeben. Durch die TS-Erweiterung des in dieser Arbeit verwendeten SM-Beobachters ist es möglich, den diskontinuierlichen Rückführterm mithilfe einer geeigneten kontinuierlichen Funktion zu approximieren und dieses Signal daraufhin zur Fehlerdiagnose auszuwerten. Dies liefert eine Methodik zur Aktor- und Sensorfehlerdiagnose nichtlinearer unsicherer Systeme. Gegenüber anderen Ansätzen erlaubt das Vorgehen eine quantitative Bestimmung und teilweise sogar exakte Rekonstruktion des Fehlersignalverlaufs. Darüber hinaus ermöglicht der Ansatz die Berechnung konstanter Fehlerschwellen direkt aus dem physikalischen Vorwissen über das betrachtete System. Durch eine Erweiterung um eine Betriebsphasenerkennung wird es möglich, die Schwellenwerte des Fehlerdiagnoseansatzes online an die aktuelle Betriebsphase anzupassen. Hierdurch ergibt sich in Betriebsphasen mit geringen Modellunsicherheiten eine deutlich erhöhte Fehlersensitivität. Zudem werden in Betriebsphasen mit großen Modellunsicherheiten Falschalarme vermieden. Die Kernidee besteht darin, die aktuelle Betriebsphase mittels eines Bayes-Klassikators in Echtzeit zu ermitteln und darüber die Fehlerschwellen an die a-priori de nierten Unsicherheiten der unterschiedlichen Betriebsphasen anzupassen. Die E ffektivität und Übertragbarkeit der vorgeschlagenen Ansätze werden einerseits am akademischen Beispiel des Pendelwagens und anderseits am Beispiel der Sensorfehlerdiagnose hydrostatisch angetriebener Radlader als praxisnahe Anwendung demonstriert.

Modeling of hybrid systems by piecewise decomposition

Piecewise linear models systems arise as mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous or discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phase portrait in different regions where each subregion is modeled as a two-dimensional linear time invariant system. Then the Takagi-Sugeno model, which is a combination of local model is calculated. The simulation results show that the Alpha partition is well-suited for dealing with such a system

Robust neurofuzzy rule base knowledge extraction and estimation using subspace decomposition combined with regularization and D-optimality

A new robust neurofuzzy model construction algorithm has been introduced for the modeling of a priori unknown dynamical systems from observed finite data sets in the form of a set of fuzzy rules. Based on a Takagi-Sugeno (T-S) inference mechanism a one to one mapping between a fuzzy rule base and a model matrix feature subspace is established. This link enables rule based knowledge to be extracted from matrix subspace to enhance model transparency. In order to achieve maximized model robustness and sparsity, a new robust extended Gram-Schmidt (G-S) method has been introduced via two effective and complementary approaches of regularization and D-optimality experimental design. Model rule bases are decomposed into orthogonal subspaces, so as to enhance model transparency with the capability of interpreting the derived rule base energy level. A locally regularized orthogonal least squares algorithm, combined with a D-optimality used for subspace based rule selection, has been extended for fuzzy rule regularization and subspace based information extraction. By using a weighting for the D-optimality cost function, the entire model construction procedure becomes automatic. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

Controlador em modo dual adaptativo robusto - DMARC

The so-called Dual Mode Adaptive Robust Control (DMARC) is proposed. The DMARC is a control strategy which interpolates the Model Reference Adaptive Control (MRAC) and the Variable Structure Model Reference Adaptive Control (VS-MRAC). The main idea is to incorporate the transient performance advantages of the VS-MRAC controller with the smoothness control signal in steady-state of the MRAC controller. Two basic algorithms are developed for the DMARC controller. In the first algorithm the controller's adjustment is made, in real time, through the variation of a parameter in the adaptation law. In the second algorithm the control law is generated, using fuzzy logic with Takagi-Sugeno s model, to obtain a combination of the MRAC and VS-MRAC control laws. In both cases, the combined control structure is shown to be robust to the parametric uncertainties and external disturbances, with a fast transient performance, practically without oscillations, and a smoothness steady-state control signal

Identificação fuzzy-multimodelos para sistemas não lineares

This paper presents a new multi-model technique of dentification in ANFIS for nonlinear systems. In this technique, the structure used is of the fuzzy Takagi-Sugeno of which the consequences are local linear models that represent the system of different points of operation and the precursors are membership functions whose adjustments are realized by the learning phase of the neuro-fuzzy ANFIS technique. The models that represent the system at different points of the operation can be found with linearization techniques like, for example, the Least Squares method that is robust against sounds and of simple application. The fuzzy system is responsible for informing the proportion of each model that should be utilized, using the membership functions. The membership functions can be adjusted by ANFIS with the use of neural network algorithms, like the back propagation error type, in such a way that the models found for each area are correctly interpolated and define an action of each model for possible entries into the system. In multi-models, the definition of action of models is known as metrics and, since this paper is based on ANFIS, it shall be denominated in ANFIS metrics. This way, ANFIS metrics is utilized to interpolate various models, composing a system to be identified. Differing from the traditional ANFIS, the created technique necessarily represents the system in various well defined regions by unaltered models whose pondered activation as per the membership functions. The selection of regions for the application of the Least Squares method is realized manually from the graphic analysis of the system behavior or from the physical characteristics of the plant. This selection serves as a base to initiate the linear model defining technique and generating the initial configuration of the membership functions. The experiments are conducted in a teaching tank, with multiple sections, designed and created to show the characteristics of the technique. The results from this tank illustrate the performance reached by the technique in task of identifying, utilizing configurations of ANFIS, comparing the developed technique with various models of simple metrics and comparing with the NNARX technique, also adapted to identification

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.