Hybrid identification of fuzzy rule‐based models

In this study, we propose a hybrid identification algorithm for a class of fuzzy rule‐based systems. The rule‐based fuzzy modeling concerns structure optimization and parameter identification using the fuzzy inference methods and hybrid structure combined with two methods of optimization theories for nonlinear systems. Two types of inference methods of a fuzzy model concern a simplified and linear type of inference. The proposed hybrid optimal identification algorithm is carried out using a combination of genetic algorithms and an improved complex method. The genetic algorithms determine initial parameters of the membership function of the premise part of the fuzzy rules. In the sequel, the improved complex method (being in essence a powerful auto‐tuning algorithm) leads to fine‐tuning of the parameters of the respective membership functions. An aggregate performance index with a weighting factor is proposed in order to achieve a balance between performance of the fuzzy model obtained for the training and testing data. Numerical examples are included to evaluate the performance of the proposed model. They are also contrasted with the performance of the fuzzy models existing in the literature. © 2002 John Wiley & Sons, Inc.     

Stable adaptive controller design of robotic manipulators via neuro‐fuzzy dynamic inversion

In this paper, a stable adaptive control approach is developed for the trajectory tracking of a robotic manipulator via neuro‐fuzzy (NF) dynamic inversion, an inverse model constructed by the dynamic neuro‐fuzzy (DNF) model with desired dynamics. The robot neuro‐fuzzy model is initially built in the Takagi‐Sugeno (TS) fuzzy framework with both structure and parameters identified through input/output (I/O) data from the robot control process, and then employed to dynamically approximate the whole robot dynamics rather than its nonlinear components as is done by static neural networks (NNs) through parameter learning algorithm. Since the NF dynamic inversion comprises a cluster of reference trajectories connecting the initial state to the desired state of the robot, the dynamic performance in the initial control stage of robot trajectory tracking can be guaranteed by choosing the optimum reference trajectory. Furthermore, the assumption that the robot states should be on a compact set can be excluded by NF dynamic inversion design. The system stability and the convergence of tracking errors are guaranteed by Lyapunov stability theory, and the learning algorithm for the DNF system is obtained thereby. Finally, the viability and effectiveness of the proposed control approach are illustrated through comparing with the dynamic NN (DNN) based control approach. © 2005 Wiley Periodicals, Inc.     

Performance evaluation of multilayer perceptron,radial basis function,fuzzy inference system,and an adaptively tuned fuzzy wavelet neural network in parameter prediction of multiphase flow measurement instrumentation

Application of predictive models in industrial multiphase flow metering has attracted an increasing attention recently. Void fraction (VF), water–liquid ratio (WLR), and flow regime are key parameters, measured by oil/water/gas multiphase flow metres (MPFM) in petroleum industry. Artificial neural networks and fuzzy inference systems (FIS) are reliable and efficient computational models, which can be simply implemented on microprocessors of MPFMs, having the advantages of trainability, adaptability, and capability to model non‐linear functions. In this paper, a wavelet‐based adaptive neuro‐FIS (WANFIS) is introduced and validated by the prediction of multiphase flow measurement critical parameters including flow regime, VF, and WLR. The performance of the proposed WANFIS model is then compared with multilayer perceptron (MLP), radial basis function (RBF) network, and an FIS trained by fuzzy c‐means and a subtractive clustering method in the prediction of flow parameters in a customized designed structure of oil/water/gas MPFM. Structural parameters of all predictive models are first optimized to yield the most efficient structure for the available dataset. Comparison is then made between the optimized predictive models, in terms of mean squared error of parameter prediction, computation time, and repeatability of the prediction process. According to the obtained results, MLP model using Levenberg–Marquardt training algorithm and WANFIS model using gradient‐based back propagation dynamical iterative learning algorithm are the most efficient models, which give the best performance compared with other used models. All predictive models can predict the flow regime with 100% accuracy, whereas the highest inaccuracy is related to the prediction of WLR. The results of this study can be used to select and develop the most appropriate predictive model applicable in predicting and identifying flow measurement parameters in industrial MPFMs.     

Multi‐objective robust fuzzy fractional order proportional–integral–derivative controller design for nonlinear hydraulic turbine governing system using evolutionary computation techniques

The present paper proposes a novel multi‐objective robust fuzzy fractional order proportional–integral–derivative (PID) controller design for nonlinear hydraulic turbine governing system (HTGS) by using evolutionary computation techniques. The fuzzy fractional order PID (FOPID) controller takes closed loop error and its fractional derivative as inputs and performs fuzzy logic operations. Then, it produces the output through the fractional order integrator. The predominant advantages of the proposed controller are its capability to handle complex nonlinear processes like HTGS in heuristic manner, due to fuzzy incorporation and extending an additional flexibility in tuning the order of fractional derivative/integral terms to enhance the closed loop performance. The present work formulates the optimal tuning problem of fuzzy FOPID controller for HTGS as a multi‐objective one instead of a traditional single‐objective one towards satisfying the conflicting criteria such as less settling time and minimum damped oscillations simultaneously to ensure the improved dynamic performance of HTGS. The multi‐objective evolutionary computation techniques such as non‐dominated sorting genetic algorithm‐II (NSGA‐II) and modified NSGA‐II have been utilized to find the optimal input/output scaling factors of the proposed controller along with the order of fractional derivative/integral terms for HTGS system under no load and load turbulence conditions. The performance of the proposed fuzzy FOPID controller is compared with PID and FOPID controllers. The simulations have been conducted to test the tracking capability and robust performance of HTGS during dynamic set point changes for a wide range of operating conditions and model parameter variations, respectively. The proposed robust fuzzy FOPID controller has ensured better fitness value and better time domain specifications than the PID and FOPID controllers, during optimization towards satisfying the conflicting objectives such as less settling time and minimum damped oscillations simultaneously, due to its special inheritance of fuzzy and FOPID properties.     

Fuzzy Identification of Nonlinear Systems via Orthogonal Transform

This paper is concerned with the application of orthogonal transforms and fuzzy competitive learning to extract fuzzy rules from data. The least square algorithm with orthogonal transforms is proposed to supervise the progress of fuzzy competitive learning. First of all, competitive learning takes place in the product space of system inputs and outputs and each cluster corresponds to a fuzzy IF–THEN rule. The fuzzy relation matrix, confirmed by fuzzy competitive learning, is studied by the orthogonal least square algorithm. The validity of fuzzy rules is obtained by analyzing the effect of orthogonal vectors in the fuzzy model, and subsequently removing less important ones. The structure identification and parameter identification of the fuzzy model are simultaneously confirmed in the proposed algorithm. Using simulation results as an example, the fuzzy model of non‐linear systems can be built by using the proposed algorithm. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

An E‐HOIM Based Data‐Driven Adaptive TILC of Nonlinear Discrete‐Time Systems for Non‐Repetitive Terminal Point Tracking

This work proposes a new adaptive terminal iterative learning control approach based on the extended concept of high‐order internal model, or E‐HOIM‐ATILC, for a nonlinear non‐affine discrete‐time system. The objective is to make the system state or output at the endpoint of each operation track a desired target value. The target value varies from one iteration to another. Before proceeding to the data‐driven design of the proposed approach, an iterative dynamical linearization is performed for the unknown nonlinear systems by using the gradient of the nonlinear system with regard to the control input as the iteration‐and‐time‐varying parameter vector of the equivalent linear I/O data model. By virtue of the basic idea of the internal model, the inverse of the parameter vector is approximated by a high‐order internal model. The proposed E‐HOIM‐ATILC does not use measurements of any intermediate points except for the control input and terminal output at the endpoint. Moreover, it is data‐driven and needs merely the terminal I/O measurements. By incorporating additional control knowledge from the known portion of the high order internal model into the learning control law, the control performance of the proposed E‐HOIM‐ATILC is improved. The convergence is shown by rigorous mathematical proof. Simulations through both a batch reactor and a coupled tank system demonstrate the effectiveness of the proposed method.     

Robust monotone gradient‐based discrete‐time iterative learning control

This paper considers the use of matrix models and the robustness of a gradient‐based iterative learning control (ILC) algorithm using both fixed learning gains and nonlinear data‐dependent gains derived from parameter optimization. The philosophy of the paper is to ensure monotonic convergence with respect to the mean‐square value of the error time series. The paper provides a complete and rigorous analysis for the systematic use of the well‐known matrix models in ILC. Matrix models provide necessary and sufficient conditions for robust monotonic convergence. They also permit the construction of accurate sufficient frequency domain conditions for robust monotonic convergence on finite time intervals for both causal and non‐causal controller dynamics. The results are compared with recently published results for robust inverse‐model‐based ILC algorithms and it is seen that the algorithm has the potential to improve the robustness to high‐frequency modelling errors, provided that resonances within the plant bandwidth have been suppressed by feedback or series compensation. Copyright © 2008 John Wiley & Sons, Ltd.     

Dynamic intermittent Q‐learning–based model‐free suboptimal co‐design of ‐stabilization

This paper proposes an intermittent model‐free learning algorithm for linear time‐invariant systems, where the control policy and transmission decisions are co‐designed simultaneously while also being subjected to worst‐case disturbances. The control policy is designed by introducing an internal dynamical system to further reduce the transmission rate and provide bandwidth flexibility in cyber‐physical systems. Moreover, a Q‐learning algorithm with two actors and a single critic structure is developed to learn the optimal parameters of a Q‐function. It is shown by using an impulsive system approach that the closed‐loop system has an asymptotically stable equilibrium and that no Zeno behavior occurs. Furthermore, a qualitative performance analysis of the model‐free dynamic intermittent framework is given and shows the degree of suboptimality concerning the optimal continuous updated controller. Finally, a numerical simulation of an unknown system is carried out to highlight the efficacy of the proposed framework.     

Structured Learning and Decomposition of Fuzzy Models for Robotic Control Applications

In this paper a specially designed structured-optimization procedure is used for learning the parameters of the Takagi–Sugeno (TS) type fuzzy models. It is well-known that the number of learning parameters increases exponentially with the number of model inputs. Therefore an appropriate learning scheme with preliminary structuring of the learning parameters into two groups: antecedent parameters and consequent parameters can be helpful for speeding-up the learning process. Two different optimization algorithms for tuning the antecedent and consequent parameters respectively are used in a sequence of repetitive loops (epochs). The stop criterion is defined as a number of repetitions of the loops or as a desired minimal error. Random walk algorithm with variable step size is used in this paper for tuning the antecedent parameters of the membership functions. For tuning the consequent parameters of the singletons, a specially proposed local learning algorithm is used. The problem of dimensionality reduction in fuzzy modeling is also considered in the paper from another viewpoint, namely as a hierarchical fuzzy model structure. It is accomplished by a decomposition of the complete fuzzy model into a feedforward hierarchical structure of sub-models called partial fuzzy models each one with two inputs and one output. Then the local models are learned separately in a preliminary specified and repetitive order. Such decomposition scheme has a potential for a significant reduction of the number of model parameters to be tuned thus reducing the total learning time. It has been experimentally shown that both concepts for dimensionality reduction in learning fuzzy models have benefits in learning speed and accuracy. A comparison with simultaneous optimization of all parameters of a single fuzzy model is also given. It shows that the proposed structured learning as well as the decomposition of the fuzzy model into a hierarchical fuzzy model structure lead to reducing the learning time and creating more accurate fuzzy models. Finally an application for learning a fuzzy controller of a two-link robot motion is shown and analysed.     

Fuzzy risk assessment of mortality after coronary surgery using combination of adaptive neuro‐fuzzy inference system and K‐means clustering

In this paper, a fuzzy expert system based on adaptive neuro‐fuzzy inference system (ANFIS) is introduced to assess the mortality after coronary bypass surgery. In preprocessing phase, the attributes were reduced using a univariant analysis in order to make the classifier system more effective. Prognostic factors with a p‐value of less than 0.05 in chi‐square or t‐student analysis were given to inputs ANFIS classifier. The correct diagnosis performance of the proposed fuzzy system was calculated in 824 samples. To demonstrate the usefulness of the proposed system, the study compared the performance of fuzzy system based on ANFIS method through the binary logistic regression with the same attributes. The experimental results showed that the fuzzy model (accuracy: 96.4%; sensitivity: 66.6%; specificity: 97.2%; and area under receiver operating characteristic curve: 0.82) consistently outperformed the logistic regression (accuracy: 89.4%; sensitivity: 47.6%; specificity: 89.4%; and area under receiver operating characteristic curve: 0.62). The obtained classification accuracy of fuzzy expert system was very promising with regard to the traditional statistical methods to predict mortality after coronary bypass surgery such as binary logistic regression model.     

Parameter estimation for block‐oriented nonlinear systems using the key term separation

This article considers the parameter estimation problems of block‐oriented nonlinear systems. By using the key term separation, the system output is represented as a linear combination of unknown parameters. We give a key term separation auxiliary model gradient‐based iterative (KT‐AM‐GI) identification algorithm and propose a key term separation auxiliary model three‐stage gradient‐based iterative (KT‐AM‐3S‐GI) identification algorithm by using the hierarchical identification principle. Meanwhile, the multiinnovation theory is used to derived the key term separation auxiliary model three‐stage multiinnovation gradient‐based iterative (KT‐AM‐3S‐MIGI) algorithm. The analysis shows that compared with the KT‐AM‐GI algorithm, the KT‐AM‐3S‐GI algorithm can improve the parameter estimation accuracy and reduce the computational burden. In addition, the KT‐AM‐3S‐MIGI can give more accurate parameter estimates than the KT‐AM‐3S‐GI algorithm and can track time‐varying parameters based on the dynamical window data. This work provides a reference for improving the identification performance of multiinput nonlinear output‐error systems or multivariable nonlinear systems. The simulation results confirm the effectiveness of the proposed algorithm.     

An efficient compensatory neuro-fuzzy system and its applications

In this study, a compensatory neuro-fuzzy system (CNFS) is proposed. The compensatory fuzzy reasoning method uses adaptive fuzzy operations of a neuro-fuzzy system to make the fuzzy logic system more adaptive and effective. Furthermore, an online learning algorithm that consists of structure learning and parameter learning is proposed to automatically construct the CNFS. The structure learning is based on the fuzzy similarity measure to determine the number of fuzzy rules, and the parameter learning is based on backpropagation algorithm to adjust the parameters. The simulation results have shown that (1) the CNFS model converges quickly and (2) the CNFS model has a lower root mean square (RMS) error than other models.     

High‐order internal model‐based iterative learning control design for nonlinear distributed parameter systems

This article deals with the problem of iterative learning control algorithm for a class of nonlinear parabolic distributed parameter systems (DPSs) with iteration‐varying desired trajectories. Here, the variation of the desired trajectories in the iteration domain is described by a high‐order internal model. According to the characteristics of the systems, the high‐order internal model‐based P‐type learning algorithm is constructed for such nonlinear DPSs, and furthermore, the corresponding convergence theorem of the presented algorithm is established. It is shown that the output trajectory can converge to the desired trajectory in the sense of (L²,λ) ‐norm along the iteration axis within arbitrarily small error. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.     

Neuro-f uzzy system modeling based on automatic f uzzy clustering

A neuro-fuzzy system model based on automatic fuzzy clustering is proposed. A hybrid model identification algorithm is also developed to decide the model structure and model parameters. The algorithm mainly includes three parts :1) Automatic fuzzy C-means (AFCM) , which is applied to generate fuzzy rules automatically , and then fix on the size of the neuro-fuzzy network , by which the complexity of system design is reducesd greatly at the price of the fitting capability; 2)Recursive least square estimation ( RLSE) . It is used to update the parameters of Takagi-Sugeno model , which is employed to describe the behavior of the system;3) Gradient descent algorithm is also proposed for the fuzzy values according to the back propagation algorithm of neural network. Finally ,modeling the dynamical equation of the two- link manipulator with the proposed approach is illustrated to validate the feasibility of the method.     

Neuro-fuzzy system modeling based on automatic fuzzy clustering

A neuro-fuzzy system model based on automatic fuzzy dustering is proposed. A hybrid model identification algorithm is also developed to decide the model structure and model parameters. The algorithm mainly includes three parts：1） Automatic fuzzy C-means （AFCM）, which is applied to generate fuzzy rttles automatically, and then fix on the size of the neuro-fuzzy network, by which the complexity of system design is reducesd greatly at the price of the fitting capability; 2） R.ecursive least square estimation （RLSE）. It is used to update the parameters of Takagi-Sugeno model, which is employed to describe the behavior of the system;3） Gradient descent algorithm is also proposed for the fuzzy values according to the back propagation algorithm of neural network. Finally,modeling the dynamical equation of the two-link manipulator with the proposed approach is illustrated to validate the feasibility of the method.     

Experimental evaluations of proportional–integral–derivative type fuzzy controllers with parameter adaptive methods for an active magnetic bearing system

Abstract: This paper deals with the experimental control of a rotating active magnetic bearing (AMB) system using proportional–integral–derivative type fuzzy controllers (PIDFCs) with parameter adaptive methods. Three kinds of parameter adaptive method, including fuzzy tuner, function tuner and relative rate observer, have been proposed in the literature for tuning the coefficients of PIDFCs. However, only a simulation comparison between these methods for control of a second‐order linear system with varying parameters and time delay has been done. In general, theoretical models need to be confirmed and modified through experimental results. This paper provides experimental verification by applying PIDFCs with self‐tuning algorithms for control of a highly nonlinear AMB system. It is shown that the steady‐state error of the AMB system using the function tuner method is lower and the first resonant frequency of the AMB system using the relative rate observer method is higher than the other two methods, and the proportional–integral–derivative controller is quite unstable. The experimental results also show that all of the tuning methods can support a high rotation frequency of the AMB system. In practice, there are only a few differences between the three kinds of parameter adaptive methods.     

Improved adaptive fault‐tolerant control design for hypersonic vehicle based on interval type‐2 T‐S model

This study proposes an improved adaptive fault estimation and accommodation algorithm for a hypersonic flight vehicle that uses an interval type‐2 Takagi‐Sugeno fuzzy model and a quantum switching module. First, an interval type‐2 Takagi‐Sugeno fuzzy model for the hypersonic flight vehicle system with elevator faults is developed to process the nonlinearity and parameter uncertainties. An improved adaptive fault estimation algorithm is then constructed by adding an adjustable parameter. The quantum switching module is also applied to the estimation part to select an appropriate algorithm in different fault cases. The estimation results from the given fuzzy observer are used to design a type‐2 fuzzy fault accommodation controller to stabilize the fuzzy system. The stability of the proposed scheme is analyzed using the Lyapunov stability theory. Finally, the validity and availability of the method are verified by a series of comparisons on numerical simulation results.     

Computationally‐Light Non‐Lifted Data‐Driven Norm‐Optimal Iterative Learning Control

Computational complexity and model dependence are two significant limitations on lifted norm optimal iterative learning control (NOILC). To overcome these two issues and retain monotonic convergence in iteration, this paper proposes a computationally‐efficient non‐lifted NOILC strategy for nonlinear discrete‐time systems via a data‐driven approach. First, an iteration‐dependent linear representation of the controlled nonlinear process is introduced by using a dynamical linearization method in the iteration direction. The non‐lifted NOILC is then proposed by utilizing the input and output measurements only, instead of relying on an explicit model of the plant. The computational complexity is reduced by avoiding matrix operation in the learning law. This greatly facilitates its practical application potential. The proposed control law executes in real‐time and utilizes more control information at previous time instants within the same iteration, which can help improve the control performance. The effectiveness of the non‐lifted data‐driven NOILC is demonstrated by rigorous analysis along with a simulation on a batch chemical reaction process.     

Robust fuzzy control for continuous perturbed time‐delay affine takagi–sugeno fuzzy models

The stability analysis and controller synthesis methodology for a continuous perturbed time‐delay affine (CPTDA) Takagi–Sugeno (T‐S) fuzzy model is proposed in this paper. The CPTDA T‐S fuzzy models include both linear nominal parts and uncertain parameters in each fuzzy rule. The proposed fuzzy control approach is developed based on an iterative linear matrix inequality (ILMI) algorithm to cope with the stability criteria and H_∞ performance constraints for the CPTDA T‐S fuzzy models. Finally, a numerical simulation for the nonlinear inverted pendulum system is given to show the application and availability of the present design approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

神经模糊系统中模糊规则的优选

提出一种基于两级聚类算法的自组织神经模糊系统，该系统采用两级聚类算法（改进的最近邻域聚类算法和Gustafson-Kessel模糊聚类算法）对输入／输出数据进行模糊聚类，并由模糊聚类的划分熵确定最优划分，建立模糊模型，模型精度可由梯度下降法进一步提高。仿真结果表明，这种神经模糊系统具有结构简单、规则数少、学习速度快以及建模精度高等特点。