L. Wang, Adaptive Fuzzy Systems and Control, Prentice-Hall, Inc. 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....between neuron activation function and fuzzy set membership. Furthermore, prediction consists of the use of a fuzzy inference engine with such rules. Due to the duality between neural network and fuzzy system present in FasArt, the universal approximation principle obtained for fuzzy systems [23] can also be applied to FasArt. Also due to this duality, inversion of the rules is straightforward, i.e. inversion of the model can be made by reverting the knowledge of direct dynamics, as it has been used for the control of other non linear plants, in which the consequents (outputs) and some ....

L. Wang, "Adaptive fuzzy systems and control", New York, NY: PTR Prentice Hall, 1994.

....engine with these rules to relate input to output. Due to the duality between neural network and fuzzy system present in FasArt, the universal approximation principle can be applied, ensuring that there exists a set of rules that allow the system to approximate any function to any given accuracy [18]. Also due to this duality, inversion of the rules is straightforward, i.e. inversion of the model can be made by reverting the knowledge of direct dynamics. Furthermore, in [6] rules partial inversion is used, in which the consequents (outputs) and some of the antecedents (state variables) are ....

....in order to reduce global error, by locally refining the least or worse teamed input output relations. This is carried out by using the descending gradient method, which vary parameters (weights) in the direction indicated by the index derivative of error with respect to the parameters vector [18]. Furthermore, a penalty method is used to reduce the influence of (maybe temporarily) wrong rules, although these rules are not completely forgotten and can be recalled if they become valid again. Due to the fact that this refining is local, and wrong rules are not forgotten completely, ....

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Wang L. "Adaptive Fuzzy Systems and Control", PTR Prentice Hall, 1994.

....approaches can only make use of numerical information. Because so much human knowledge is represented in linguistic terms, incorporating it into an engineering system in a systematic and efficient manner is very important. However, linguistic information can be represented in fuzzy terms [5]. A fuzzy logic system representation has the ability to incorporate the human knowledge, represented in linguistic terms, into the engineering system very efficiently. Fuzzy logic systems are constructed from fuzzy IF THEN rules. Representing the process to be controlled as a fuzzy logic system ....

Wang, L. Adaptive Fuzzy Systems And Control. Prentice-Hall, Inc., 1994.

....to class a otherwise. 7) The cost function (6) can be minimized by many different techniques. In our experiments, the FBF network parameters (i.e. 9 ) were obtained by performing a gradient descent with respect to the MSE across the training set. The learning formulas are as follows [3, 10]: 26610 FI 3i (8) H 9 ; 198 9 ghX FI li g 9 Fm li g ; FIH 9 ; i n J 9 (9) J 9 ; 195 9 ghX FY li g 9 FI li gh ; FIH 9 ; i J 9 (10) cfe cKk c o are the learning rates of 9 9 . ....

L. X. Wang. Adaptive Fuzzy Systems and Control. Prentice Hall, Englewood Cliffs, New Jersey, 1994.

.... systems) Some of these systems share important characteristics with neural networks, such as the Multi Layer Perceptron (MLP) 22] e.g. the feed forward architecture, the capability of learning free parameters from numerical data sets, the universal function approximation capability [12, 8, 24, 25], and the approximation of the Bayes classifier [16] Moreover, the available linguistic knowledge (even not complete) can be incorporated into a fuzzy inference system before the learning procedure, in order to speed up the training phase. In this paper, we study the structure identification ....

....a fuzzy inference system before the learning procedure, in order to speed up the training phase. In this paper, we study the structure identification problem in a Multi Input Multi Output (MIMO) neuro fuzzy system constituted by a network of Fuzzy Basis Functions (FBF s) previously presented in [8, 23, 9, 25], holding the universal function approximation property and the capability of learning from examples. In addition, the FBF network permits one to build a non parametric classifier able to approximate the Bayes discriminant function. At a glance, FBF networks seem to be special cases of Radial ....

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Wang, L. X. Adaptive Fuzzy Systems and Control. Prentice Hall, 1994. Captions for Tables

....that is adequate to the expected accuracy of the system. Reducing the structure of a KBNN can be achieved through regular pruning of nodes and connections thus allowing for knowledge to emerge in the structure, or through aggregating nodes into bigger rule clusters. The former approach is used in [19,21,38,39,41,44,46,47,53]. The latter one is explored in this paper. It is based on a regular aggregation of rule nodes in the KBNN structure, which is equivalent to aggregating rules into rule clusters before new data and new knowledge is accommodated in the system. This is the case with the EFuNNs. Different KBNNs are ....

L.X. Wang, Adaptive Fuzzy Systems and Control, Prentice Hall, Englewood Cliffs, NJ, 1994.

....that is adequate to the expected accuracy of the system. Reducing the structure of a KBNN can be achieved through regular pruning of nodes and connections thus allowing for knowledge to emerge in the structure, or through aggregating nodes into bigger rule clusters. The former approach is used in [19,21,38,39,41,44,46,47,53]. The latter one is explored in this paper. It is based on a regular aggregation of rule nodes in the KBNN structure, which is equivalent to aggregating rules into rule clusters before new data and new knowledge is accommodated in the system. This is the case with the EFuNNs. Di erent KBNNs are ....

L.X. Wang, Adaptive Fuzzy Systems and Control, Prentice Hall, Englewood Cli!s, NJ, 1994.

....possibility to interpret and understand knowledge. From this point of view, the combination of neural networks (learning capabilities) and fuzzy systems (natural language) seems very promising. Most of these systems realize a fuzzy controller by a neural network, e.g. 2] 3] 4] 5] 6] 7] [8], 9] by translating the concepts of fuzzy control to neural networks and exploit learning algorithms like backpropagation. These fusions of neuro and fuzzy are based on some compromises. On one hand, special neural networks are used that tend to lose the basic property of distributed ....

L. Wang, Adaptive Fuzzy Systems and Control, Prentice--Hall, 1994.

....of the problems associated to large scale dynamic systems justifies the slow progresses concerning formal results. It should be stressed that IC techniques attempt to control complex systems without oversimplifying or even without using a model. Nevertheless, important advances have been made [Wang94, NarPar90], denoting the increasing maturity of the field. I believe that the advantages of fuzzy logic are more relevant at the decision making levels, where it has the potential to successfully replace binary logic based Expert Controllers, than as an alternative to low level controllers. Neural networks ....

L.-X. Wang, Adaptive Fuzzy Systems and Control, Prentice-Hall, 1994

....Fuzzy modeling had also been recognized as a practical strategy for control and for modeling. Fuzzy models had been very attractive for its capability to capture expert knowledge. In the recent years many algorithms to generate fuzzy models starting from Input Output data have been developed [11] [9] Nowadays new algorithms permit the combination of numerical and expert information in the same framework [6] A framework for non linear system identification using fuzzy models has been proposed in [14] 15] The algorithms presented in [15] and [6] guarantee that the obtained fuzzy model ....

.... ae minf 1 l (u 1 ) 2 l (u 2 ) N i l (uN i )g using MIN operator 1 l (u 1 ) Delta 2 l (u 2 ) Delta : Delta N i l (uN i ) using PRODUCT operator (2) The training of these models or the extraction of the model using inputoutput data has been treated extensively in [11][9] 6] In the present work the linear structure of the consequences of the rules is exploited to generate a fuzzy Intelligent Control model with fixed antecedents where only the consequences are calculated. For N input output data the inference process can be represented as 2 6 6 6 4 y 1 y ....

Wang L.X. 1994, Adaptive Fuzzy Systems and Control, Prentice Hall, USA.

....models belong to the most popular model structures used. From the input output view, fuzzy systems are flexible mathematical functions which can approximate other functions or just data (measurements) with a desired accuracy. This property is called general function approximation (Kosko, 1994; Wang, 1994; Zeng and Singh, 1995) Compared to other well known approximation techniques such as artificial neural networks, fuzzy systems provide a more transparent representation of the system under study, which is mainly due to the possible linguistic interpretation in the form of rules. The logical ....

Wang, L.-X. (1994). Adaptive Fuzzy Systems and Control, Design and Stability Analysis.New Jersey: Prentice Hall.

....of evolutionary computation, it is difficult to prove analytically the stability of the evolutionary fuzzy controller. Thus we can not guarantee the asymptotic stability of the presented controller. But, by introducing the supervisory control input which is popular in adaptive fuzzy control[2], we can restrict the derivative of the proper Lyapunov function V to be negative semi definite. If V is negative semi definite, the state of the system remains bounded. Thus when the evolution is progressed, the mobile robot system can move with a stable control input plus the supervisory ....

....This problem is equivalent to the optimization problem to minimize V under constraint V = GammakV . On the other hand, if there exist an optimal control input u that satisfies the above constraint for a given system, then we can also design a fuzzy logic system that approximate u [2]. It is widely known that the knowledge of human experts can be described with fuzzy rules in a fuzzy logic system. Specifically, each piece of human knowledge is represented by using the fuzzy IF THEN rules: R (l) If x 1 is F l 1 , x n is F l n , THEN u is l , where x = x 1 ; ....

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Li-Xin Wang, "Adaptive Fuzzy Systems and Control", Prentice Hall Int. Inc, 1994

....controllers based on nonlinear models are desirable. Fuzzy modeling is a well developed and attractive nonlinear modeling technique due to its capability to capture expert knowledge. In recent years many algorithms have been developed to generate fuzzy models starting from InputOutput data [12], 10] 7] Nowadays new algorithms permit the combination of numerical and expert information in the same framework [6] Also a framework for non linear system identification using fuzzy models has been proposed in [15] 16] The wide acceptance of these two strategies motivated the formulation ....

Wang L.X. 1994, Adaptive Fuzzy Systems and Control, Prentice Hall, USA.

....their meaning, but a fuzzy set directly. Therefore, a linguistic model is a system description in the form of a linguistic rule set interpretable by human beings, which is a desirable characteristic in some problems. 1. 2 STRUCTURE OF A LINGUISTIC MODEL The basic structure of a linguistic model [31] is showed in Fig. 1.1. Interface Fuzzification Inference System real input x Interface Defuzzification Knowledge Base output x real Data Base Rule Base Figure 1.1 Structure of a linguistic model The Knowledge Base (KB) is the component containing the knowledge about the system ....

Wang, L.X., Adaptive Fuzzy Systems and Control, Prentice-Hall, 1994.

....modes of reasoning which are approximate and analog rather than exact. II.B Types of Fuzzy Rule Based Systems Two di erent types of FRBSs are usually distinguished in the specialized literature according to the form of the fuzzy rules considered and to the types of inputs and outputs used [9]. We shall introduce them in the next subsections. II.B.1 Mamdani Fuzzy Rule Based Systems This type of FRBS was proposed by Mamdani [10] who was able to translate Zadeh s preliminary assumptions to the rst FRBS applied to a control problem. These kinds of Fuzzy Systems, the ones most used ....

Wang, L. X. (1994). \Adaptive fuzzy systems and control." Prentice-Hall.

....use of linguistic descriptions. Although the earliest work by Prof. Zadeh on fuzzy systems has not received as much attention as it deserved in early 1960s, since then the methodology has become a welldeveloped framework. The typical architectures of fuzzy inference systems are those introduced by Wang (1994, 1997) Takagi and Sugeno (1985) and Jang, Sun and Mizutani (1997) Wang (1994) constructs a fuzzy system having Gaussian membership functions, product inference rule and weighted average defuzzifier. This architecture is accepted as the standard method in most applications. Takagi and Sugeno ....

....systems has not received as much attention as it deserved in early 1960s, since then the methodology has become a welldeveloped framework. The typical architectures of fuzzy inference systems are those introduced by Wang (1994, 1997) Takagi and Sugeno (1985) and Jang, Sun and Mizutani (1997) Wang (1994) constructs a fuzzy system having Gaussian membership functions, product inference rule and weighted average defuzzifier. This architecture is accepted as the standard method in most applications. Takagi and Sugeno (1985) change the defuzzification 4 procedure where dynamic systems are used in ....

WANG, L. X., 1994, Adaptive Fuzzy Systems and Control, Design and Stability Analysis (New Jersey: PTR Prentice Hall).

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L. Wang, Adaptive Fuzzy Systems and Control, Prentice-Hall, Inc. 1994.

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L.X. Wang, Adaptive Fuzzy Systems and Control (Prentice Hall, 1994).

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L. X. Wang, Adaptive Fuzzy Systems and Control, Prentice Hall, 1994.

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L. X. Wang, Adaptive Fuzzy Systems and Control, Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1994.

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L.X. Wang, "Adaptive Fuzzy Systems and Control", Prentice Hall, New Jersey, 1994.

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L.X. Wang (1994): Adaptive Fuzzy Systems and Control, Prentice-Hall, Englewood-Cliffs.

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L. Wang, Adaptive fuzzy systems and control, Prentice Hall, Englewood Cliffs, 1994.

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L.X. Wang, Adaptive Fuzzy Systems and Control, Englewood Cliffs, N.J.: Prentice-Hall, 1994.

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L.X. Wang, Adaptive Fuzzy Systems and Control, Englewood Cliffs, N.J.: Prentice-Hall, 1994.

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