Number Of Fuzzy Rules Research Articles

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.

Design Minimum Rule-Base Fuzzy Inference Nonlinear Controller for Second Order Nonlinear System

This research is focused on proposed minimum rule base PID computed torque algorithms with application to continuum robot manipulator. The stability of the closed-loop system is proved mathematically based on the Lyapunov method. Classical Computed Torque Controller (CTC) is robust to control model partly uncertainties and external disturbances. This controller is one of the significant nonlinear methodologies; according to the nonlinear dynamic formulation. One of the main targets in this research is increase the robustness based on the artificial intelligence methodology. Classical computed torque control has difficulty in handling unstructured model uncertainties. One can overcome this problem by combining a computed torque controller and artificial intelligence (e.g. fuzzy logic). To approximate a time-varying nonlinear dynamic system, a fuzzy system requires a large amount of fuzzy rule base. This large number of fuzzy rules will cause a high computation load. To reduce the number of rule base this research is focused on the PD like fuzzy plus integral methodology. This method is applied to continuum robot manipulator to have the best performance.

Modeling and OnLine Control of Nonlinear Systems using Neuro-Fuzzy Learning tuned by Metaheuristic Algorithms

This paper proposes a hybrid learning algorithm for tuning an Adaptive Network based Fuzzy Inference System ANFIS. The proposed scheme of adapting parameters in ANFIS employs evolutionary techniques PSO and GA to adjust the antecedent parameters. The leastsquares (LSE) algorithm is used to adjust consequent parameters. The number of fuzzy rules is fixed and given by using the Xie Beni’s index. This new approach is applied to identify and control nonlinear systems with an on-line strategy. The obtained results are compared to similar ANFIS using gradient descent method GD as antecedent parameters of training algorithm and other methods applied in the same problems.

A recurrent neural fuzzy controller based on self‐organizing improved particle swarm optimization for a magnetic levitation system

SummaryThis paper proposes a recurrent neural fuzzy controller (RNFC) approach based on a self‐organizing improved particle swarm optimization (SOIPSO) algorithm used for solving control problems. The proposed SOIPSO algorithm can adaptively determine the number of fuzzy rules and automatically adjust the parameters in an RNFC. The proposed learning algorithm consisted of phases of structure and parameter learning. Structure learning adopts several subswarms to constitute the adjustable variables in fuzzy systems, and an elite‐based structure strategy determines the suitable number of fuzzy rules. This paper proposes an improved particle swarm optimization technique, which consists of the modified evolutionary direction operator (MEDO) and traditional PSO techniques. The proposed MEDO method used the EDO and migration operation to improve the search ability of a global solution. Finally, the proposed RNFC approach based on the SOIPSO learning algorithm (RNFC–SOIPSO) was adopted to control a magnetic levitation system. Experimental results demonstrated that the proposed RNFC–SOIPSO model outperforms other models. Copyright © 2014 John Wiley & Sons, Ltd.

Dynamic T‐S Fuzzy Systems Identification Based on Sparse Regularization

AbstractFuzzy system identification suffers from rules explosion, i.e., a large number of fuzzy rules are required for fuzzy systems with high dimension input variable. In this paper, a dynamic algorithm is proposed to address T‐S fuzzy system identification with both sparsity and dynamic clustering, named as dynamic sparse fuzzy inference systems (D‐sparseFIS). Due to two different estimation approaches of fuzzy rule consequence parameter, i.e., global estimation and local estimation, D‐sparseFIS.local and D‐sparseFIS.global methods are exploited with local least squares and global least squares estimation based on sparse regularization. Both two dynamic algorithms can guarantee a minimal number of fuzzy rules and nonzero consequence parameters are equipped in T‐S fuzzy system. Finally, some numerical experiments are presented to illustrate the effectiveness of the proposed algorithms.

Linear matrix inequalities‐based membership‐function‐dependent stability analysis for non‐parallel distributed compensation fuzzy‐model‐based control systems

This study investigates the stability of fuzzy-model-based (FMB) control system, which is formed by a Takagi–Sugeno (T–S) fuzzy model representing a non-linear plant and a fuzzy controller connected in a closed loop. The proposed fuzzy controller considers a higher design flexibility that the premise membership functions and the number of fuzzy rules are allowed to be not the same as those of the T–S fuzzy model. By employing simple membership functions and a smaller number of fuzzy rules, the complexity of the fuzzy controller can be reduced to facilitate its implementation. Based on the Lyapunov stability theory, a membership-function-dependent (MFD) stability analysis is proposed to develop stability conditions in the form of linear matrix inequalities (LMIs) to determine the system stability and facilitate the control synthesis. The information of the membership functions is brought to the MFD LMI-based stability conditions, which are dedicated to the FMB control system under consideration. It is thus the proposed MFD stability analysis result is more relaxed compared with the existing membership-function-independent stability analysis results. A simulation example is given to illustrate the effectiveness of the proposed approach.

Event-based control for memristive systems

This paper studies the event-based control for memristive systems. Consider the state-dependent properties of the memristor, a new fuzzy model employing parallel distributed compensation (PDC) gives a new way to linearize complicated memristive system with only two subsystems. As the existence of uncertainties of memristor and to reduce the amount of communication, event-based control algorithm to stabilize memristive systems and extend the results to systems with signal quantization and networked induced delays. Through the fuzzy modeling and distributed event-based control, there are three main advantages: (1) only two linear subsystems are considered to reduce the numbers of fuzzy rules from 2n to 2×n as for traditional Takagi–Sugeno fuzzy model, n is the number of memristive subsystems; (2) the memristive subsystem is triggered at its own event time, which reduces communication burdens and lowers the controller updating frequency; (3) the effects of quantization and time delays are taken into account.

Pragmatical adaptive synchronization – New fuzzy model of two different and complex chaotic systems by new adaptive control

In this paper, (1) a new fuzzy model is presented to simulate two different chaotic systems with different numbers of nonlinear terms and (2) a new adaptive approach and a new control Lyapunov function are proposed to synchronize these two different fuzzy chaotic systems and speed up the convergence of errors. By using this new model, the numbers of fuzzy rules of chaotic systems can be reduced from 2N to 2×N and only 2 subsystems are needed, where N is the number of nonlinear terms. The fuzzy systems become much simpler. In addition, through the new fuzzy model, the new fuzzy systems are much simpler than T–S fuzzy systems (when nonlinear systems are complicated) and can be used to any other kind of application in fuzzy logic control or fuzzy modeling. Mathieu–Van der Pol system (which is called M–V system in this paper) and Quantum cellular neural networks nanosystem (which is called Q-CNN system in this paper) are used for illustrations in numerical simulation results to show the effectiveness and feasibility of our new adaptive approach and new control Lyapunov function. The T–S fuzzy modeling and traditional adaptive control are also given in Appendices B and C for comparison.

Design New Robust Self Tuning Fuzzy Backstopping Methodology

This research is focused on proposed Proportional-Integral (PI) like fuzzy adaptive backstopping fuzzy algorithms based on Proportional- Derivative (PD) fuzzy rule base with the adaptation laws derived in the Lyapunov sense. Adaptive SISO PI like fuzzy adaptive backstopping fuzzy method has two main objectives; the first objective is design a SISO fuzzy system to compensate for the model uncertainties of the system, and the second objective is focused on the design PI like fuzzy controller based on PD method as an adaptive methodology. Classical backstopping control is robust to control model uncertainties and external disturbances and is a main controller in this research. The fuzzy controller is used in this method to system compensation. To increase the robust of this controller adaptive PI like fuzzy controller is introduced and applied to backstopping fuzzy controller. Classical backstopping control method has difficulty in handling unstructured model uncertainties. One can overcome this problem by combining a backstopping controller and artificial intelligence (e.g. fuzzy logic). To approximate a time-varying nonlinear dynamic system, a fuzzy system requires a large amount of fuzzy rule base. This large number of fuzzy rules will cause a high computation load. The addition of an adaptive law to a backstopping fuzzy controller to online tune the coefficients in use will ensure a moderate computational load. The adaptive laws in this algorithm are designed based on the Lyapunov stability theorem. This method is applied to continuum robot manipulator to have the best performance.

On Line Tuning Premise and Consequence FIS Based on Lyaponuv Theory with Application to Continuum Robot

Classical sliding mode controller is robust to model uncertainties and external disturbances. A sliding mode control method with a switching control low guarantees asymptotic stability of the system, but the addition of the switching control law introduces chattering in to the system. One way of attenuating chattering is to insert a saturation function inside of a boundary layer around the sliding surface. Unfortunately, this addition disrupts Lyapunov stability of the closed-loop system. Classical sliding mode control method has difficulty in handling unstructured model uncertainties. One can overcome this problem by combining a sliding mode controller and fuzzy system together. Fuzzy rules allow fuzzy systems to approximate arbitrary continuous functions. To approximate a time-varying nonlinear system, a fuzzy system requires a large amount of fuzzy rules. This large number of fuzzy rules will cause a high computation load. The addition of an adaptive law to a fuzzy sliding mode controller to online tune the parameters of the fuzzy rules in use will ensure a moderate computational load. Refer to this research; tuning methodology can online adjust both the premise and the consequence parts of the fuzzy rules. Since this algorithm for is specifically applied to a robot manipulator.

Optimal design of T–S fuzzy controller for a nonlinear system using a new adaptive particle swarm optimization algorithm

Designing an optimal Takagi–Sugeno (T–S) fuzzy system for real–world non–linear control problems is a challenging problem. Complex non–linear system produces large fuzzy rule–based and requires large amount of memory. To overcome these problems, this paper proposes a hybrid approach to generate the optimal T–S fuzzy system. First, the Fuzzy Clustering Method (FCM) is employed to partitioning the input space and extracting initial fuzzy rule–based. Moreover, a new Adaptive Particle Swarm Optimization (APSO) technique is suggested to determine the optimal number of clusters in FCM, which is the same as the number of fuzzy rules. Finally, Recursive Least Square (RLS) method based on the Mean Square Errors (MSE) criterion is used to regulate the coefficients of the consequent part of initial fuzzy rules. Some simulations are conducted on a Non–Linear Inverted Pendulum (NLIP) system to support the efficiency of the proposed approach in designing compact and accurate T–S fuzzy systems.

Online Tuning of Power System Stabilizers Using Fuzzy Logic Network with Fuzzy C-Means Clustering Prediction: A Case Study

Power system stabilizers (PSS) has been widely used to enhance damping due to the electromechanical low frequency oscillations occurrence in power systems. In this paper, a new method is used for the online tuning of parameters of conventional power system stabilizers (CPSS) using fuzzy logic. Fuzzy logic enables mathematical modeling and computation of some nonlinear parameters of the system, which are usually derived empirically by utilization of expert knowledge rules. Various literatures has shown that fuzzy logic controller is one of the most useful methods for expert knowledge utilization. This type of controller is adaptive in nature and can be used successfully as a power system stabilizer. The design of fuzzy logic controllers is mainly based on fuzzy rules and input/output membership functions. Simple and efficient clustering algorithms allow data classification in distinct groups using distance and/or similarity functions. In the present paper, the optimum generation of fuzzy rules base using Fuzzy C-means (FCM) clustering technique is used. In fact, data are classified and the number of fuzzy rules which depends on convergence radius is determined. Finally, the performance of proposed FCM controller is compared with that of conventional controller. The active power, reactive power and bus voltages used as inputs to the fuzzy logic network based power system stabilizer and the parameters of the optimum stabilizer , i.e. gain factor as well as time constants of the lead/lag compensator, are the outputs of the proposed system. The design method has been successfully implemented on a single machine power system connected to an infinite bus over various operating conditions.

Fuzzy Prediction of Molten Iron Silicon Content in BF Based on Hierarchical System

A hierarchical fuzzy system model is presented based on data driving, and then, the model is used to predict the molten iron silicon content in BF. As input variables this model uses the control parameters of a current BF such as moisture, pulverized coal injection, oxygen addition, coke ratio etc. And variables employed to develop the model have been obtained from data collected online from Blast Furnace of Baotou Steel plant. This paper utilizes the fuzzy clustering algorithm combined nearest neighbor clustering and fuzzy c-means clustering to classify the input space. The simulation and error results show that the prediction based on hierarchical fuzzy model and data-driven method has good approximation and fit the output characteristics of the system. The most important point is that the number of fuzzy rules is greatly reduced.

Optimal GainsTuning of Speed Controller in Induction Motor Drives Using Particle SWARMOptimization

The last decade has witnessed a great interest in using evolutionary algorithms (EAs), such as genetic algorithms (GA), evolutionary strategies and particle swarm optimization (PSO), for multivariate optimization. This paper presents a modern approach of speed control for three-phase induction motor (IM) using PSO algorithm to optimize the parameters of the proportional integral (PI) and Fuzzy-PI controllers. Comparison between different controllers is achieved, using PI and fuzzy-PI controllers which are tuned by two methods, firstly manually and secondly using PSO technique. Hybrid of FL and PI controller PSO-based for the speed control of given motor is also performed to eliminate the drawbacks of PI controller (overshoot, undershoot) and FL controller (steady-state error), which has a minimum number of fuzzy rules and membership functions (MFs). The overall system is simulated under various operating conditions and experimental results are prepared.

SCOLS-FuM: A Hybrid Fuzzy Modeling Method for Telecommunications Time-Series Forecasting

An application of fuzzy modeling to the problem of telecommunications time-series prediction is proposed in this paper. The model building process is a two-stage sequential algorithm, based on Subtractive Clustering (SC) and the Orthogonal Least Squares (OLS) techniques. Particularly, the SC is first employed to partition the input space and determine the number of fuzzy rules and the premise parameters. In the sequel, an orthogonal estimator determines the input terms which should be included in the consequent part of each fuzzy rule and calculate their parameters. A comparative analysis with well-established forecasting models is conducted on real world telecommunications data, where the characteristics of the proposed forecaster are highlighted.

Mamdani and Takagi-Sugeno fuzzy classifier accuracy improvement using enhanced particle swarm optimization

This paper discusses a method for designing a fuzzy-rule-based classifiers using enhanced particle swarm optimization EPSO. Two different fuzzy classifiers are considered and optimized. The first classifier is based on Mamdani fuzzy inference system M_EPSO fuzzy classifier. The second classifier is based on Takagi-Sugeno fuzzy inference system TS_EPSO fuzzy classifier. The parameters of the proposed fuzzy classifiers including premise antecedent parameters, consequent parameters and structure of fuzzy rules are optimized using EPSO. The performances of M_EPSO and TS_EPSO fuzzy classifiers are compared to commonly used fuzzy based classifiers. Experimental results show that higher classification accuracy can be obtained with limited number of fuzzy rules by using the proposed EPSO fuzzy classifiers. Another comparison that shows the consistency of EPSO for optimizing the proposed fuzzy classifiers over other evolutionary algorithms is also presented.

Computed force control system using functional link radial basis function network with asymmetric membership function for piezo‐flexural nanopositioning stage

A computed force control system using functional link radial basis function network with asymmetric membership function (FLRBFN-AMF) for three-dimension motion control of a piezo-flexural nanopositioning stage (PFNS) is proposed in this study. First, the dynamics of the PFNS mechanism with the introduction of a lumped uncertainty including the equivalent hysteresis friction force are derived. Then, a computed force control system with an auxiliary control is proposed for the tracking of the reference contours with improved steady-state response. Since the dynamic characteristics of the PFNS are non-linear and time varying, a computed force control system using FLRBFN-AMF is designed to improve the control performance for the tracking of various reference trajectories, where the FLRBFN-AMF is employed to estimate a non-linear function including the lumped uncertainty of the PFNS. Moreover, by using the asymmetric membership function, the learning capability of the networks can be upgraded and the number of fuzzy rules can be optimised for the functional link radial basis function network. Furthermore, the adaptive learning algorithms for the training of the parameters of the FLRBFN-AMF online are derived using the Lyapunov stability theorem. Finally, some experimental results for the tracking of various reference contours of the PFNS are given to demonstrate the validity of the proposed control system.

A Hybrid Learning Method for Constructing Compact Rule-Based Fuzzy Models

The Takagi–Sugeno–Kang-type rule-based fuzzy model has found many applications in different fields; a major challenge is, however, to build a compact model with optimized model parameters which leads to satisfactory model performance. To produce a compact model, most existing approaches mainly focus on selecting an appropriate number of fuzzy rules. In contrast, this paper considers not only the selection of fuzzy rules but also the structure of each rule premise and consequent, leading to the development of a novel compact rule-based fuzzy model. Here, each fuzzy rule is associated with two sets of input attributes, in which the first is used for constructing the rule premise and the other is employed in the rule consequent. A new hybrid learning method combining the modified harmony search method with a fast recursive algorithm is hereby proposed to determine the structure and the parameters for the rule premises and consequents. This is a hard mixed-integer nonlinear optimization problem, and the proposed hybrid method solves the problem by employing an embedded framework, leading to a significantly reduced number of model parameters and a small number of fuzzy rules with each being as simple as possible. Results from three examples are presented to demonstrate the compactness (in terms of the number of model parameters and the number of rules) and the performance of the fuzzy models obtained by the proposed hybrid learning method, in comparison with other techniques from the literature.

Hierarchical Structured Sparse Representation for T–S Fuzzy Systems Identification

“The curse of dimensionality” has become a significant bottleneck for fuzzy system identification and approximation. In this paper, we cast the Takagi-Sugeno (T-S) fuzzy system identification into a hierarchical sparse representation problem, where our goal is to establish a T-S fuzzy system with a minimal number of fuzzy rules, which simultaneously have a minimal number of nonzero consequent parameters. The proposed method, which is called hierarchical sparse fuzzy inference systems ( H-sparseFIS), explicitly takes into account the block-structured information that exists in the T-S fuzzy model and works in an intuitive way: First, initial fuzzy rule antecedent part is extracted automatically by an iterative vector quantization clustering method; then, with block-structured sparse representation, the main important fuzzy rules are selected, and the redundant ones are eliminated for better model accuracy and generalization performance; moreover, we simplify the selected fuzzy rules consequent with sparse regularization such that more consequent parameters can approximate to zero. This algorithm is very efficient and shows good performance in well-known benchmark datasets and real-world problems.

Algorithms of the tradeoff between accuracy and complexity in the design of fuzzy approximators

Two important stages in design of fuzzy approximators, including structure generation and parameter optimization, are considered. Two optimization criteria, i.e., the accuracy measured by the root-mean-square error and the complexity expressed as the number of fuzzy rules, are proposed. The results of studies of the approximators obtained on real data from the KEEL repository are given, and the results are compared with their analogs.