Sum Normal Optimization of Fuzzy Membership Functions

Given a fuzzy logic system, how can we determine the membership functions that will result in the best performance? If we constrain the membership functions to a certain shape (e.g., triangles or trapezoids) then each membership function can be parameterized by a small number of variables and the membership optimization problem can be reduced to a parameter optimization problem. This is the approach that is typically taken, but it results in membership functions that are not (in general) sum normal. That is, the resulting membership function values do not add up to one at each point in the domain. This optimization approach is modified in this paper so that the resulting membership functions are sum normal. Sum normality is desirable not only for its intuitive appeal but also for computational reasons in the real time implementation of fuzzy logic systems. The sum normal constraint is applied in this paper to both gradient descent optimization and Kalman filter optimization of fuzzy membership functions. The methods are illustrated on a fuzzy automotive cruise controller

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

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

H-infinity Estimation for Fuzzy Membership Function Optimization

Given a fuzzy logic system, how can we determine the membership functions that will result in the best performance? If we constrain the membership functions to a specific shape (e.g., triangles or trapezoids) then each membership function can be parameterized by a few variables and the membership optimization problem can be reduced to a parameter optimization problem. The parameter optimization problem can then be formulated as a nonlinear filtering problem. In this paper we solve the nonlinear filtering problem using H∞ state estimation theory. However, the membership functions that result from this approach are not (in general) sum normal. That is, the membership function values do not add up to one at each point in the domain. We therefore modify the H∞ filter with the addition of state constraints so that the resulting membership functions are sum normal. Sum normality may be desirable not only for its intuitive appeal but also for computational reasons in the real time implementation of fuzzy logic systems. The methods proposed in this paper are illustrated on a fuzzy automotive cruise controller and compared to Kalman filtering based optimization

Cardiomyopathy Detection from Electrocardiogram Features

Cardiomyopathy means heart (cardio) muscle (myo) disease (pathy) . Currently, cardiomyopathies are defined as myocardial disorders in which the heart muscle is structurally and/or functionally abnormal in the absence of a coronary artery disease, hypertension, valvular heart disease or congenital heart disease sufficient to cause the observed myocardial abnormalities. This book provides a comprehensive, state-of-the-art review of the current knowledge of cardiomyopathies. Instead of following the classic interdisciplinary division, the entire cardiovascular system is presented as a functional unity, and the contributors explore pathophysiological mechanisms from different perspectives, including genetics, molecular biology, electrophysiology, invasive and non-invasive cardiology, imaging methods and surgery. In order to provide a balanced medical view, this book was edited by a clinical cardiologist

ROBUST STABILIZATION AND OPTIMIZATION OF FLIGHT CONTROL SYSTEM WITH STATE FEEDBACK AND FUZZY LOGICS

This paper deals with combination of two powerful and modern control tools as linear matrix inequality that is used for synthesis a ‘crisp’ controller and a fuzzy control approach for designing a soft controller. The control design consists of two stages. The first stage investigates the problem of a robust an H2 controller design with parameters uncertainties of the handled plant in the presence of external disturbances. Stability onditions are obtained via a quadratic Lyapunov function and represented in the form of linear matrix inequalities. The second stage consists of the outer loop controller construction based on fuzzy inference system that utilizes for altitude hold mode. The parameters of the fuzzy controller are adjusted with a gradient descent method in order to improve the performance of the overall system. The case study illustrates the efficiency of the proposed approach to the flight control of small Unmanned Aerial Vehicle.Розглянуто принцип поєднання двох потужних та сучасних засобів теорії управління як метод лінійних матричних нерівностей, який використовується для синтезу чіткого регулятора та нечіткого управління для синтезу регулятора з м’якими обчисленнями. Процедура синтезу складається з двох етапів. На першому етапі вирішено задачу синтезу робастного H2 - регулятора для безпілотного літального апарату із врахуванням зовнішніх збурень, які діють на об’єкт управління. Умови стійкості сформовано у вигляді лінійних матричних нерівностей. Другий етап присвячено задачі синтезу нечіткого регулятора для зовнішнього контуру управління в режимі стабілізації висоти, заснованого на нечіткій логіці. З метою покращення якості управління параметри нечіткого регулятора настроюються за допомогою градієнтного методу. Проведено дослідження на прикладі управління поздовжнім каналом безпілотного літального апарату