Membership Functions Of Fuzzy System Research Articles

Event-based [formula omitted] load frequency control for fuzzy Markov-jump IPS with wind power under hybrid attacks

This paper addresses the H∞ load frequency control problem of interconnected power systems that incorporate high-permeability wind power and face a mixed attack of deception and denial of service. The interconnected power system is modeled as a Takagi–Sugeno (T–S) fuzzy Markov jump system. Given the involvement of wind power, optimizing the utilization of already in-demand communication resources becomes imperative. Thus, a new event-triggering mechanism is adopted to reduce data transmission traffic. Simultaneously, in response to the general network’s vulnerability to network attacks in power systems, a closed-loop system with Markov jump, modeled using the T–S fuzzy approach, is studied. A novel multi-agent Event-Triggering Strategy (ETS) composed of membership functions is proposed to address the mismatch between the membership functions of fuzzy systems and fuzzy controllers, and ensure the consistency of multi-agent systems. Subsequently, employing Lyapunov–Krasovskii theory and stochastic analysis techniques, conditions sufficient to ensure the asymptotic stability of interconnected power systems are derived from linear matrix inequalities. Finally, simulation verification is provided to ensure the accuracy and feasibility of the obtained theory.

Choose the suitable fuzzy membership function in prediction of diameter of nanofibers produced from electrospinning using fuzzy logic system as artificial intelligence technique

Fuzzy logic System is used to predict some parameters. In this system the crisp data were converted into fuzzy data using membership function. There are many members ship function used in fuzzy system to fuzzify data. In this search, nanofibers were obtained by electrospinning process and scanned by SEM. Nanofiber’s diameters were predicted as output of the system using all membership functions in fuzzy system by Matlab. The parameters of electrospinning process were constant except electrospinning room temperature. A comparison has been made among the predicted data using different membership functions. One membership function had been selected based on minimum error in prediction of data. It had been cleared that the best membership function was Gauss function.

Сравнительный анализ эффективности использования треугольной и трапециевидной функций принадлежности в нечетких системах принятия решений

The article is devoted to assessing the efficiency of using triangular and trapezoidal membership functions in fuzzy systems. Two metrics are proposed: execution time of the fuzzy inference algorithm, dispersion of the output value. The results of experiments on testing three fuzzy systems of different architecture complexity are presented: determining the size of a tip for a waiter; forecasting changes in energy consumption in the production system; driver assistance on the roads.

Co-design of scheduling protocol and fuzzy sliding mode controller under communication constraints

This paper investigates the co-design of scheduling protocol and sliding mode controller for interval type-2 T–S fuzzy systems under communication constraints. To reduce the transmission burden and relieve the data congestion, a stochastic scheduling protocol is established via Markov chain to determine the transmission of system state, under which only one sensor node is permitted to transmit the state signal at each instant. Different from the existing results, the key feature of the proposed protocol is that the transition probability matrix of Markov chain is co-designed with the controller, rather than given a priori. Moreover, the scheduling signal (also called token) reflecting the selected node is integrated to design a token-dependent sliding mode controller, where controller’s membership functions are constructed based on the available state. By establishing the relation between the membership functions in fuzzy system and the ones in controller, sufficient conditions are obtained to attain the stochastic stability of the closed-loop system and the reachability of the sliding domain. Moreover, an iterative optimization algorithm is proposed to search token-dependent parameters and sliding matrix with the objective of reducing the sliding domain. Finally, the effectiveness of the co-design control scheme is verified via simulation examples.

Adaptation of Number of Filters in the Convolution Layer of a Convolutional Neural Network Using the Fuzzy Gravitational Search Algorithm Method and Type-1 Fuzzy Logic

This paper presents a model of the search for adaptation of parameters and the creation of the membership functions of various fuzzy systems created using the fuzzy gravitational algorithm (FGSA). These fuzzy systems were created to find the optimal number of filters to enter a convolutional neural network (CNN) with an architecture of two convolution layers, as well as two pooling layers respectively and a classification layer, which is responsible for recognizing images. With this model, the results obtained by optimizing this CNN with the FGSA algorithm and the adaptation of parameters using this same algorithm are compared to form the membership functions of fuzzy systems. Both methods and their results are comparing with each other.

Choose the suitable fuzzy membership function in prediction of diameter of nanofibers produced from electrospinning using fuzzy logic system as artificial intelligence technique

Fuzzy logic System is used to predict some parameters. In this system the crisp data were converted into fuzzy data using membership function. There are many members ship function used in fuzzy system to fuzzify data. In this search, nanofibers were obtained by electrospinning process and scanned by SEM.
 Nanofiber’s diameters were predicted as output of the system using all membership functions in fuzzy system by Matlab. The parameters of electrospinning process were constant except electrospinning room temperature. A comparison has been made among the predicted data using different membership functions. One membership function had been selected based on minimum error in prediction of data. It had been cleared that the best membership function was Gauss function.

Event-Based $H_\infty$ Control for Discrete-Time Fuzzy Markov Jump Systems Subject to DoS Attacks

This paper is concerned with H control problem for discrete-time Takagi-Sugeno (T-S) fuzzy Markov jump systems with event-triggering scheme (ETS) and denial-of-service (DoS) attacks. Aperiodic DoS characterized by duration and frequency is introduced. In the light of DoS attacks and event-triggered fuzzy controller, the switched fuzzy Markov jump closed-loop system is established. Particularly, in order to address the issue of mismatched behavior between membership functions of fuzzy system and fuzzy controller, a novel ETS consisting of membership functions is developed. Then with the help of multiple Lyapunov function method and iterative technique, some sufficient conditions are provided to ensure the H performance of the resulting closed-loop system. Subsequently, the explicit parameter design of controller and ETS are provided. Finally, an example is employed to verify the validity of the proposed theoretical method.

Design of a fault detection and diagnose system for intelligent unmanned aerial vehicle navigation system

A secure control system is of great importance for unmanned aerial vehicles, especially in the condition of fault data injection. As the source of the feedback control system, the Inertial navigation system/Global position system (INS/GPS) is the premise of flight control system security. However, unmanned aerial vehicles have the requirement of lightweight and low cost for airborne equipment, which makes redundant device object unrealistic. Therefore, the method of fault detection and diagnosis is desperately needed. In this paper, a fault detection and diagnosis method based on fuzzy system and neural network is proposed. Fuzzy system does not depend on the mathematical model of the process, which overcomes the difficulties in obtaining the accurate model of unmanned aerial vehicles. Neural network has a strong self-learning ability, which could be used to optimize the membership function of fuzzy system. This paper is structured as follows: first, a Kalman filter observer is introduced to calculate the residual sequences caused by different sensor faults. Then, the sequences are transmitted to the fault detection and diagnosis system and fault type can be obtained. The proposed fault detection and diagnosis algorithm was implemented and evaluated with real datasets, and the results demonstrate that the proposed method can detect the sensor faults successfully with high levels of accuracy and efficiency.

Takagi–Sugeno Dynamic Neuro-Fuzzy Controller of Uncertain Nonlinear Systems

The identification problem incorporated in feedback control of uncertain nonlinear systems exhibiting complex behavior has been solved in different ways. Some of these solutions have used artificial intelligence methods like fuzzy logic and neural networks. However, their individual implementation suffers from certain drawbacks, such as the black-box nature of neural network and the problem of finding suitable membership functions for fuzzy systems. These weaknesses can be avoided by implementing a hybrid structure combining these two approaches, the so-called neuro-fuzzy system. In this paper, a neuro-fuzzy system that implements differential neural networks (DNNs) as consequences of Takagi–Sugeno (T–S) fuzzy inference rules is proposed. The DNNs substitute the local linear systems that are used in the common T–S method. In this paper, DNNs are used to provide an effective instrument for dealing with the identification of the uncertain nonlinear system, while the T–S rules are used to provide the framework of previous knowledge of the system. The main idea is to carry out an online identification process of an uncertain nonlinear system with the aim to design a closed-loop trajectory tracking controller. The methodology developed in this study that supports the identification and trajectory control designs is based on the Lyapunov formalism. The DNN implementation results in a time-varying T–S system. As a consequence, the solution of two time-varying Riccati equations was used to adjust the learning laws in the DNN as well as to adjust the gains of the controller. Two results were provided to justify the existence of positive-definite solutions for the class of Riccati equations used in the learning laws of DNNs. A complete description of the learning laws used for the set of DNN identifiers is also obtained. An autonomous underwater vehicle system is used to demonstrate the performance of the controller on tracking a desired 3-D path by this combination of the DNN and the T–S system.

Fuzzy Control Model and Simulation for Nonlinear Supply Chain System with Lead Times

A new fuzzy robust control strategy for the nonlinear supply chain system in the presence of lead times is proposed. Based on Takagi-Sugeno fuzzy control system, the fuzzy control model of the nonlinear supply chain system with lead times is constructed. Additionally, we design a fuzzy robust H∞ control strategy taking the definition of maximal overlapped-rules group into consideration to restrain the impacts such as those caused by lead times, switching actions among submodels, and customers’ stochastic demands. This control strategy can not only guarantee that the nonlinear supply chain system is robustly asymptotically stable but also realize soft switching among subsystems of the nonlinear supply chain to make the less fluctuation of the system variables by introducing the membership function of fuzzy system. The comparisons between the proposed fuzzy robust H∞ control strategy and the robust H∞ control strategy are finally illustrated through numerical simulations on a two-stage nonlinear supply chain with lead times.

Modified CLPSO-based fuzzy classification system: Color image segmentation

Fuzzy segmentation is an effective way of segmenting out objects in images containing varying illumination. In this paper, a modified method based on the Comprehensive Learning Particle Swarm Optimization (CLPSO) is proposed for pixel classification in HSI color space by selecting a fuzzy classification system with minimum number of fuzzy rules and minimum number of incorrectly classified patterns. In the CLPSObased method, each individual of population is considered to automatically generate a fuzzy classification system. Afterwards, an individual member tries to maximize a fitness criterion which is high classification rate and small number of fuzzy rules. To reduce the multidimensional search space for an M-class classification problem, the centroid of each class is calculated and then fixed in membership function of fuzzy system. The performance of the proposed method is evaluated in terms of future classification within the RoboCup soccer environment with spatially varying illumination intensities on the scene. The results present 85.8% accuracy in terms of classification.

Application of fuzzy subtractive clustering for optimal transient performance of automatic generation control in restructured power system

Nowadays, Automatic Generation Control AGC is a very impressive problem in restructured power system operation for providing electric power with high quality and reliability. In this paper, the three-area multi-units system has chosen for the AGC in restructured power system. Federal energy regulatory commission FERC supports an open market system for price based operation. The theory of DISCO participation matrix is used to simulate the bilateral contracts in the three area multi-units systems. In this paper Fuzzy logic damping controller FLDC for optimal transient performance of AGC has been used. An effective method, namely, Fuzzy Subtractive Clustering is used here, which reduces the number of rules and membership functions of Fuzzy system. This Method provides a mechanism to obtain the reduced rule set covering the whole input/ output space as well as membership functions for each input variable. Finally the results have been compared.

Adaptive Fuzzy Sliding Mode Control Based on Genetic Optimization for Rotary Steering Drilling Stabilized Platform

Considering the robust control of stabilized platform of rotary steering drilling system, an adaptive fuzzy sliding mode control strategy based on genetic optimization is presented. Firstly, the universal approximation property of fuzzy system is used to approximate the uncertain external disturbance upper bound of stabilized platform under wording condition. Subsequently, sliding mode controller is designed to guarantee the robustness of the closed-loop system and sign function is replaced by bipolar sigmoid function to weaken chattering. Finally, genetic algorithm (GA) is applied to search the optimal controller parameters, including switching function coefficient, membership function of fuzzy system, adaptive coefficient of fuzzy system and sigmoid function coefficient. Simulation results show that this control strategy can make stabilized platform achieve optimal control performance and robustness.

잡음 구분에 의한 지능형 기동표적 추적기법

본 논문에서는 기동표적의 위치 오차값 보상 기법을 이용한 지능형 기동표적 추적 기법을 제안한다. 기동표적의 관측값과 예상위치와의 차이를 가속도와 순수 잡음으로 분리한다. 최적의 수준으로 가속도를 추출하기 위하여 K-means 클러스터링 기법과 TS 퍼지 시스템을 이용한다. K-means 클러스터링에 의해 분리된 가속도와 잡음에 대한 소속함수를 설정하고 퍼지 모델화하여 기동표적의 특성을 파악한다. 계산상의 오차를 보상하기 위하여 분리된 가속도와 잡음은 추적 알고리즘의 계산과정에 적절히 이용된다. 추정값 계산시, 가속도를 분리 하므로써 필터링 과정은 표적의 비선형 기동을 선형기동으로 인식하여 칼만필터의 성능을 유지시킨다. 기동표적의 비선형성에 대한 오차는 추정된 가속도를 통해 보상된다. 제안된 시스템의 소속함수에 사용되는 파라미터값을 조종하여 상황에 따라 적응성과 강인성을 향상시킨다. 제안된 시스템은 실시간 추적이 가능하도록 구성하였으며, 몇 가지 예를 통하여 본 논문에서 제안한 방법의 우수성을 증명한다. This paper presents the intelligent tracking method for maneuvering target using the positional error compensation of the maneuvering target. The difference between measured point and predict point is separated into acceleration and noise. K-means clustering and TS fuzzy system are used to get the optimal acceleration value. The membership function is determined for acceleration and noise which are divided by K-means clustering and the characteristics of the maneuvering target is figured out. Divided acceleration and noise are used in the tracking algorithm to compensate computational error. While calculating expected value, the non-linearity of the maneuvering target is recognized as linear one by dividing acceleration and the capability of Kalman filter is kept in the filtering process. The error for the non-linearity is compensated by approximated acceleration. The proposed system improves the adaptiveness and the robustness by adjusting the parameters in the membership function of fuzzy system. Procedures of the proposed algorithm can be implemented as an on-line system. Finally, some examples are provided to show the effectiveness of the proposed algorithm.

A new fuzzy sliding mode controller for load frequency control of large hydropower plant using particle swarm optimization algorithm and Kalman estimator

SUMMARYThe load frequency control (LFC) is very important in power system operation and control for supplying sufficient, reliable, and high‐quality electric power. The conventional LFC uses an integral controller. In this paper, a new control system based on the fuzzy sliding mode controller is proposed for controlling the load frequency of nonlinear model of a hydropower plant, and this control system is compared with the proportional–integral controller and the conventional sliding mode controller. To regulate the membership functions of fuzzy system more accurately, the particle swarm optimization algorithm is also applied. Moreover, because of the unavailability of the control system variables, a nonlinear estimator is suggested for estimating and identifying the system state variables. This estimator provides the physical realization of the method and will reduce the costs of implementation. The proposed control method is performed for the LFC of hydropower plant of Karoon‐3 in Shahrekord, Iran. The simulation results show the capability of the controller system in controlling local network frequency. Copyright © 2011 John Wiley & Sons, Ltd.

A new control system design for a small hydro-power plant based on particle swarm optimization-fuzzy sliding mode controller with Kalman estimator

One of the main problems in small hydro-power plants that are locally used is their frequency control system. In this paper, a suggested control system based on the fuzzy sliding mode controller is presented for controlling the network frequency. Also, the proposed control strategy is compared with a PI controller and conventional sliding mode controller. In order to regulate the membership functions of fuzzy system more accurately, the particle swarm optimization algorithm is also applied. Moreover, because of unavailability of the control system variables, an estimator is suggested for estimating and identifying the system variables. This estimator will reduce the costs of implementing the control method. The simulation results show the ability of controller system in controlling the local network frequency in the presence of load and parameter’s variations.

Circuit implementation of high-resolution rational-powered membership functions in standard CMOS technology

This paper proposes the method to implement a general form of membership functions for fuzzy systems in CMOS technology. These membership functions are a general form of triangular types and those functions which are used in linguistic hedge fuzzy logic, hence can offer better performance in almost all applications. The comparison between the proposed method and previously reported works shows better performance in all parameters. Designed circuits to implement these types of membership functions are simulated using HSPICE by level 49 parameters (BSIM3v3) in 0.35 μm standard CMOS technology. Current mode realization of the circuits leads to simple and intuitive configurations. The Rational Power Generator Module (RPGM) generates powers with the resolution of 0.03125 and using seven programming bits. The simulation results of RPGM demonstrate a RMS error of 1.42% and a maximum power consumption of 1.05 mW.

The relationship between the uniform approximation rates and the shapes of fuzzy sets in fuzzy systems

PurposeThe purpose of this paper is to answer the question that what the best shape of fuzzy sets is in fuzzy systems for function approximation which is essential in many applications of fuzzy systems.Design/methodology/approachThe uniform approximation rates indicate the approximating capabilities of fuzzy systems for function approximation. By Fourier analysis, the uniform approximation rates are estimated for the fuzzy systems with various shapes of if‐part fuzzy sets in the case of single‐input and single‐output. Based on the approximation rates, the relationships between the approximating capabilities and the shapes of fuzzy sets are developed and compared.FindingsThe since functions as the input membership functions in fuzzy systems are proved to have the almost best approximation property in a particular class of membership functions.Research limitations/implicationsFrom the viewpoint of function approximation, the input membership functions are not necessarily positive in fuzzy systems.Practical implicationsFor engineers, the sinc‐shaped membership function is a good choice to improve their fuzzy systems in real applications.Originality/valueThe uniform approximation rates of fuzzy systems for function approximation are estimated. Mathematically, the relationships between the approximating capabilities and the shapes of fuzzy sets are analyzed for fuzzy systems.

Fuzzy rule extraction by bacterial memetic algorithms

In our previous papers, fuzzy model identification methods were discussed. The bacterial evolutionary algorithm for extracting fuzzy rule base from a training set was presented. The Levenberg–Marquardt method was also proposed for determining membership functions in fuzzy systems. The combination of the evolutionary and the gradient-based learning techniques is usually called memetic algorithm. In this paper, a new kind of memetic algorithm, the bacterial memetic algorithm, is introduced for fuzzy rule extraction. The paper presents how the bacterial evolutionary algorithm can be improved with the Levenberg–Marquardt technique. © 2009 Wiley Periodicals, Inc.

Intelligent mobile manipulator navigation using adaptive neuro-fuzzy systems

The work presented in this paper deals with the problem of autonomous and intelligent navigation of mobile manipulator, where the unavailability of a complete mathematical model of robot systems and uncertainties of sensor data make the used of approximate reasoning to the design of autonomous motion control very attractive. A modular fuzzy navigation method in changing and dynamic unstructured environments has been developed. For a manipulator arm, we apply the robust adaptive fuzzy reactive motion planning developed in [J.B. Mbede, X. Huang, M. Wang, Robust neuro-fuzzy sensor-based motion control among dynamic obstacles for robot manipulators, IEEE Transactions on Fuzzy Systems 11 (2) (2003) 249–261]. But for the vehicle platform, we combine the advantages of probabilistic roadmap as global planner and fuzzy reactive based on idea of elastic band. This fuzzy local planner based on a computational efficient processing scheme maintains a permanent flexible path between two nodes in network generated by a probabilistic roadmap approach. In order to consider the compatibility of stabilization, mobilization and manipulation, we add the input of system stability in vehicle fuzzy navigation so that the mobile manipulator can avoid stably unknown and/or dynamic obstacles. The purpose of an integration of robust controller and modified Elman neural network (MENN) is to deal with uncertainties, which can be translated in the output membership functions of fuzzy systems.