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## Neuro-fuzzy modeling and control (1995)

Venue: | IEEE PROCEEDINGS |

Citations: | 239 - 1 self |

### Citations

5157 | Optimization by simulated annealing
- Kirkpatrick, Gelatt, et al.
- 1983
(Show Context)
Citation Context ... modeling are summarized here. For complex control problems with perfect plant models, we can always use gradient-free optimization schemes, such as genetic algorithms [22], [19], simulated annealing =-=[44]-=-, [45], downhill Simplex method [68], and random method [63]. In particular, use of genetic algorithms for neural network controllers can be found in [112]; for fuzzy logic controllers, see [39], [52]... |

3886 |
Adaptation in Natural and Artificial Systems
- Holland
(Show Context)
Citation Context ...earning algorithm in neuro-fuzzy modeling are summarized here. For complex control problems with perfect plant models, we can always use gradient-free optimization schemes, such as genetic algorithms =-=[22]-=-, [19], simulated annealing [44], [45], downhill Simplex method [68], and random method [63]. In particular, use of genetic algorithms for neural network controllers can be found in [112]; for fuzzy l... |

3698 |
Learning internal representations by error propagation
- Rumelhart, Hinton, et al.
- 1986
(Show Context)
Citation Context ... Since the error signals are obtained sequentially from the output layer back to the input layer, this learning paradigm is called the back-propagation learning rule by Rumelhart, Hinton and Williams =-=[79]-=-. The gradient vector is defined as the derivative of the error measure with respect to each parameter, so we have to apply the chain rule again to find the gradient vector. If ff is a parameter of th... |

2843 |
Genetic algorithms in search, optimization, and machine learning,”
- Goldberg
- 1989
(Show Context)
Citation Context ...g algorithm in neuro-fuzzy modeling are summarized here. For complex control problems with perfect plant models, we can always use gradient-free optimization schemes, such as genetic algorithms [22], =-=[19]-=-, simulated annealing [44], [45], downhill Simplex method [68], and random method [63]. In particular, use of genetic algorithms for neural network controllers can be found in [112]; for fuzzy logic c... |

2556 |
A simplex method for function minimization.
- Nelder, Mead
- 1965
(Show Context)
Citation Context ...omplex control problems with perfect plant models, we can always use gradient-free optimization schemes, such as genetic algorithms [22], [19], simulated annealing [44], [45], downhill Simplex method =-=[68]-=-, and random method [63]. In particular, use of genetic algorithms for neural network controllers can be found in [112]; for fuzzy logic controllers, see [39], [52], [38]. If the plant model is not av... |

2081 |
System Identification: Theory for the User,
- Ljung
- 1987
(Show Context)
Citation Context ... A) \Gamma1 A T B; (42) where A T is the transpose of A and (A T A) \Gamma1 A T is the pseudo-inverse of A if A T A is non-singular. Of course, we can also employ the recursive LSE formula [23], [1], =-=[58]-=-. Specifically, let the i-th row vector of matrix A defined in equation (41) be a T i and the i-th element of B be b T i ; then ` can be calculated iteratively as follows: ` i+1 = ` i + S i+1 a i+1 (b... |

1932 |
An Algorithm for the Least-Squares Estimation of Nonlinear Parameters,"
- Marquardt
- 1963
(Show Context)
Citation Context ...ssion in statistics literature, and there are a number of other techniques for either linear or nonlinear regression, such as the GuassNewton method (linearization method) and the Marquardt procedure =-=[61]-=-. These methods can be found in advanced textbooks on regression and they are also viable techniques for finding optimal parameters in adaptive networks. E. Neural Networks as Special Cases of Adaptiv... |

1880 |
Adaptive Filter Theory”,
- Haykin
- 2002
(Show Context)
Citation Context ...o identify the linear parameters. 5. Sequential (approximate) LSE only: The outputs of an adaptive network are linearized with respect to its parameters, and then the extended Kalman filter algorithm =-=[21]-=- is employed to update all parameters. This method has been proposed in the neural network literature [85], [84], [83]. The choice of one of the above methods should be based on a trade-off between co... |

1651 |
Fuzzy identification of systems and its application to modelling and control,
- Takagi, Sugeno
- 1985
(Show Context)
Citation Context ...ystems, and computer vision. Because of its multi-disciplinary nature, the fuzzy inference system is known by a number of names, such as fuzzy-rule-based system, fuzzy expert system [37], fuzzy model =-=[97]-=-, [90], fuzzy associative memory [47], fuzzy logic controller [60], [49], [50], and simply (and ambiguously) fuzzy system. The basic structure of a fuzzy inference system consists of three conceptual ... |

1321 |
Applied nonlinear control
- Slotine, Li
- 1991
(Show Context)
Citation Context ...a fuzzy inference system, is equipped with enough parameters to approximate f . For the second task, we need to apply the concept of a branch of nonlinear control theory called sliding control [101], =-=[86]-=-. The standard approach is to define an error metrics as s(t) = ( d dt + ) n\Gamma1 e(t); withs? 0: (66) The equation s(t) = 0 defines a time varying hyperplane in R n on which the tracking error vect... |

900 | ANFIS: Adaptive-Network-Based Fuzzy Inference System”,
- Jang
- 1993
(Show Context)
Citation Context ...ch transition along the gradient direction in the parameter space. Usually we can change the step size to vary the speed of convergence; two heuristic rules for updating the value ofsare described in =-=[29]-=-. When an n-node feedforward network is represented in its topological order, we can envision the error measure E p as the output of an additional node with index n+1, whose node function fn+1 can be ... |

875 |
Fuzzy Sets and Systems, Theory and Applications,
- Dubois, Prade
- 1980
(Show Context)
Citation Context ... (a) two fuzzy sets A and B; (b) A; (c) A [B; (d) A " B. Note that other consistent definitions for fuzzy AND and OR have been proposed in the literature under the names T-norm and T-conorm opera=-=tors [16], respectively. Except fo-=-r min and max, none of these operators satisfy the law of distributivity: A[(B"C) (x) =s(A[B)"(A[C) (x); A"(B[C) (x) =s(A"B)[(A"C) (x): However, min and max do incur some diff... |

801 | The Cascade-Correlation Learning Architecture",
- Fahlman, Lebiere
- 1990
(Show Context)
Citation Context ...Sugeno's iterative method [91] and various clustering algorithms proposed by Chiu [15], Khedkar [43] and Wang [104]. Moreover, advances on the constructive and destructive learning of neural networks =-=[18]-=-, [53] can also shed some lights on this problem. Though we can speed up the parameter identification problem by introducing the least-squares estimator into the learning cycle, gradient descent still... |

753 |
Fuzzy logic in control systems: fuzzy logic controller – part II.
- Lee
- 1990
(Show Context)
Citation Context ...s these two interpretations of a fuzzy rule A ! B. Here we shall adopt the first interpretation, where A ! B implies A coupled with B. The treatment of the second interpretation can be found in [34], =-=[49]-=-, [50]. Y A B (a) X Y A B X (b) Fig. 5. Two interpretations of fuzzy implication: (a) A coupled with B; (b) A entails B.. C. Fuzzy Reasoning (Approximate Reasoning) Fuzzy reasoning (also known as appr... |

729 |
An experiment in linguistic synthesis with a fuzzy logic controller,”
- Mamdani, Assilian
- 1975
(Show Context)
Citation Context ...ure, the fuzzy inference system is known by a number of names, such as fuzzy-rule-based system, fuzzy expert system [37], fuzzy model [97], [90], fuzzy associative memory [47], fuzzy logic controller =-=[60]-=-, [49], [50], and simply (and ambiguously) fuzzy system. The basic structure of a fuzzy inference system consists of three conceptual components: a rule base, which contains a selection of fuzzy rules... |

612 |
Fast learning in network of locally-tuned processing units,"
- 8Moody, Darken
- 1989
(Show Context)
Citation Context ...is a well-known structure that has been studied in the regions of the cerebral cortex, the visual cortex, and so forth. Drawing on the knowledge of biological receptive fields, Moody and Darken [66], =-=[67]-=- proposed a network structure that employs local receptive fields to perform function mappings. Similar schemes have been proposed by Powell [74], Broomhead and Lowe [7], and many others in the areas ... |

603 |
Neuronlike adaptive elements that can solve difficult learning control problems.
- Barto, Sutton, et al.
- 1983
(Show Context)
Citation Context ...of genetic algorithms for neural network controllers can be found in [112]; for fuzzy logic controllers, see [39], [52], [38]. If the plant model is not available, we can apply reinforcement learning =-=[2]-=- to find a working controller directly. The close relationship between reinforcement learning and dynamic programming was addressed in [3], [109]. Other variants of reinforcement learning includes tem... |

601 |
Multivariable functional interpolation and adaptive networks,
- Broomhead, Lowe
- 1988
(Show Context)
Citation Context ...ields, Moody and Darken [66], [67] proposed a network structure that employs local receptive fields to perform function mappings. Similar schemes have been proposed by Powell [74], Broomhead and Lowe =-=[7]-=-, and many others in the areas of interpolation and approximation theory; these schemes are collectively called radial basis function approximations. Here we shall call this network structure the radi... |

448 |
Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence.
- Kosko
- 1992
(Show Context)
Citation Context ...of its multi-disciplinary nature, the fuzzy inference system is known by a number of names, such as fuzzy-rule-based system, fuzzy expert system [37], fuzzy model [97], [90], fuzzy associative memory =-=[47]-=-, fuzzy logic controller [60], [49], [50], and simply (and ambiguously) fuzzy system. The basic structure of a fuzzy inference system consists of three conceptual components: a rule base, which contai... |

435 |
Othogonal least squares learning algorithm for radial basis function networks,"
- Chen, C, et al.
- 1991
(Show Context)
Citation Context ...o the first several nearest neighbors of ~c i 's). Once these nonlinear parameters are fixed, the linear parameters can be found by either the least-squares method or the gradient method. Chen et al. =-=[8]-=- used an alternative method that employs the orthogonal least-squares algorithm to determine the c i 's and f i 's while keeping the oe i 's at a predetermined constant. An extension of Moody-Darken's... |

391 |
Oscillation and chaos in physiological control systems.
- Mackey, Glass
- 1997
(Show Context)
Citation Context ...d of a constant: f i = ~a i \Delta ~x + b i ; (51) where ~a i is a parameter vector and b i is a scalar parameter. Stokbro et al. [88] used this structure to model the MackeyGlass chaotic time series =-=[59]-=- and found that this extended version performed better than the original RBFN with the same number of fitting parameters. It was pointed out by the authors that under certain constraints, the RBFN is ... |

378 |
and D.Wang, “Variable structure systems with sliding mode,”
- Utkin, Wang
- 1977
(Show Context)
Citation Context ...ork or a fuzzy inference system, is equipped with enough parameters to approximate f . For the second task, we need to apply the concept of a branch of nonlinear control theory called sliding control =-=[101]-=-, [86]. The standard approach is to define an error metrics as s(t) = ( d dt + ) n\Gamma1 e(t); withs? 0: (66) The equation s(t) = 0 defines a time varying hyperplane in R n on which the tracking erro... |

358 |
Radial basis functions for multivariate interpolation: A review." In
- Powell
- 1987
(Show Context)
Citation Context ...of biological receptive fields, Moody and Darken [66], [67] proposed a network structure that employs local receptive fields to perform function mappings. Similar schemes have been proposed by Powell =-=[74]-=-, Broomhead and Lowe [7], and many others in the areas of interpolation and approximation theory; these schemes are collectively called radial basis function approximations. Here we shall call this ne... |

347 |
Principles of neurodynamics: perceptrons and the theory of brain mechanisms,
- Rosenblatt
- 1961
(Show Context)
Citation Context ... \Gamma e \Gammax 1 + e \Gammax : Identity function: f(x) = x: When the step function (hard-limiter) is used as the activation function for a layered network, the network is often called a perceptron =-=[78]-=-, [70], as explained in example 4. For a neural network to approximate a continuous-10 0 10 -2 -1 0 1 2 (a) step function -10 0 10 -2 -1 0 1 2 (b) sigmoid function -10 0 10 -2 -1 0 1 2 (c) hyper-tange... |

342 |
Adaptive Filtering Prediction and Control,
- Sin
- 1984
(Show Context)
Citation Context ... old data pairs must decay as new data pairs become available. Again, this problem is well studied in the adaptive control and system identification literature and a number of solutions are available =-=[20]-=-. One simple method is to formulate the squared error measure as a weighted version that gives higher weighting factors to more recent data pairs. This amounts to the addition of a forgetting factorst... |

319 |
Fuzzy Model Identification Based on Cluster Estimation”,
- Chiu
- 1994
(Show Context)
Citation Context ...ction includes Jang's fuzzy CART approach [30], Lin's reinforcement learning method [55], Sun's fuzzy k-d trees [92], Sugeno's iterative method [91] and various clustering algorithms proposed by Chiu =-=[15]-=-, Khedkar [43] and Wang [104]. Moreover, advances on the constructive and destructive learning of neural networks [18], [53] can also shed some lights on this problem. Though we can speed up the param... |

317 |
Faster-Learning Variations on Back-Propagation: An Empirical Study,”
- Fahlman
- 1989
(Show Context)
Citation Context ...hms hold equally true for both neural networks and fuzzy models. Variants of gradient descent proposed in the neural network literature; including second-order back-propagation [72], quickpropagation =-=[17]-=-, and so on, can be used to speed up training. A number of techniques used in nonlinear regression can also contribute in this regard, such as the GuassNewton method (linearization method) and the Mar... |

314 |
Adaptive Pattern Recognition and Neural Networks (Addison-Wesley,
- Pao
- 1989
(Show Context)
Citation Context ...mension of the search space of the original back-propagation method. If we fix the membership functions and adapt only the consequent part, then ANFIS can be viewed as a functional-link network [46], =-=[71] where the "enh-=-anced representations " of the input variables are obtained via the membership functions. These "enhanced representations", which take advantage of human knowledge, apparently express m... |

304 |
A hierarchical neural network model for control, and learning of voluntary movement
- Kawato, Furukawa, et al.
- 1987
(Show Context)
Citation Context ...ges of the plant's inputs and outputs during two consecutive time instants. Other similar methods that aim at using an approximate Jacobian matrix to achieve the same learning effects can be found in =-=[41]-=-, [11], [102]. Applying specialized learning to find an ANFIS controller for the inverted pendulum was reported in [27]. desired model + - e x x (k+1) d + - e x x (k+1) d controller ANFIS plant x(k) x... |

252 |
A Fuzzy-Logic-Based Approach to Qualitative Modeling”,
- Sugeno, Yasukawa
- 1993
(Show Context)
Citation Context ...active research topic in the field. Work along this direction includes Jang's fuzzy CART approach [30], Lin's reinforcement learning method [55], Sun's fuzzy k-d trees [92], Sugeno's iterative method =-=[91]-=- and various clustering algorithms proposed by Chiu [15], Khedkar [43] and Wang [104]. Moreover, advances on the constructive and destructive learning of neural networks [18], [53] can also shed some ... |

231 |
Nonlinear signal processing using neural networks: prediction and system modeling.
- Lapedes, Farber
- 1987
(Show Context)
Citation Context ...s) \Gamma 0:1x(t): (59) The prediction of future values of this time series is a benchmark problem that has been used and reported by a number of connectionist researchers, such as Lapedes and Farber =-=[48]-=-, Moody [67], [65], Jones et al. [35], Crower [77], and Sanger [81]. The simulation results presented here were reported in [33], [29]; more details can be found therein. The goal of the task is to us... |

230 | Gaussian Networks for Direct Adaptive Control,"
- Sanner, Slotine
- 1991
(Show Context)
Citation Context ...cted to feedback linearizable systems. The reader is referred to [86] for a more detailed treatment of this subject. Applications of this technique to neural network and fuzzy control can be found in =-=[82]-=- and [103], respectively. 26 F. Gain Scheduling Under certain arrangements, the first-order Sugeno fuzzy model becomes a gain scheduler that switches between several sets of feedback gains. For instan... |

225 |
Computer Controlled Systems: Theory and Design.
- Astrom, Wittenmark
- 1984
(Show Context)
Citation Context ... (A T A) \Gamma1 A T B; (42) where A T is the transpose of A and (A T A) \Gamma1 A T is the pseudo-inverse of A if A T A is non-singular. Of course, we can also employ the recursive LSE formula [23], =-=[1]-=-, [58]. Specifically, let the i-th row vector of matrix A defined in equation (41) be a T i and the i-th element of B be b T i ; then ` can be calculated iteratively as follows: ` i+1 = ` i + S i+1 a ... |

205 | Learning and Sequential Decision Making,"
- Barto, Sutton, et al.
- 1989
(Show Context)
Citation Context ...t model is not available, we can apply reinforcement learning [2] to find a working controller directly. The close relationship between reinforcement learning and dynamic programming was addressed in =-=[3]-=-, [109]. Other variants of reinforcement learning includes temporal difference methods (TD() algorithms) and Q-learning [107]. Representative applications of reinforcement learning to fuzzy control ca... |

196 |
Structure identification of fuzzy models",
- Sugeno, Kang
- 1988
(Show Context)
Citation Context ..., and computer vision. Because of its multi-disciplinary nature, the fuzzy inference system is known by a number of names, such as fuzzy-rule-based system, fuzzy expert system [37], fuzzy model [97], =-=[90]-=-, fuzzy associative memory [47], fuzzy logic controller [60], [49], [50], and simply (and ambiguously) fuzzy system. The basic structure of a fuzzy inference system consists of three conceptual compon... |

187 |
Learning and Tuning Fuzzy Logic Controller through Reinforcements,
- Berenji, Khedkar
- 1992
(Show Context)
Citation Context ... variants of reinforcement learning includes temporal difference methods (TD() algorithms) and Q-learning [107]. Representative applications of reinforcement learning to fuzzy control can be found in =-=[4]-=-, [51], [12], [57]. Some other design and analysis approaches for fuzzy controllers include cell-to-cell mapping techniques [13], [87], model-based design method [98], self-organizing controllers [75]... |

176 |
Industrial Applications of Fuzzy Control,
- Sugeno
- 1985
(Show Context)
Citation Context ...60], Sendai subway systems [116], container ship crane control [115], elevator control [54], nuclear reaction control [5], automobile transmission control [40], aircraft control [14], and many others =-=[89]-=-. With the availability of learning algorithms, a wider range of applications is expected. Note that this approach is not only for control applications. If the target system to be emulated is a human ... |

169 | Functional equivalence between radial basis function networks and fuzzy inference systems,”
- Jang, Sun
- 1993
(Show Context)
Citation Context ...specified by an MF of a step function crossing at the constant. Moreover, a zero-order Sugeno fuzzy model is functionally equivalent to a radial basis function network under certain minor constraints =-=[32]-=-. It should be pointed out that the output of a zero-order Sugeno model is a smooth function of its input variables as long as the neighboring MF's in the premise have enough overlap. In other words, ... |

160 |
Neural-network-based fuzzy logic control and decision system,”
- Lin, Lee
- 1991
(Show Context)
Citation Context ... with two rules; (b) equivalent ANFIS architecture. with an application example of chaotic time series prediction. Note that similar network structures were also proposed independently by Lin and Lee =-=[56]-=- and Wang and Mendel [105]). A. ANFIS Architecture For simplicity, we assume the fuzzy inference system under consideration has two inputs x and y and one output z. For a first-order Sugeno fuzzy mode... |

148 |
Stability analysis and design of fuzzy control systems,”
- Sugeno
- 1992
(Show Context)
Citation Context ...g to fuzzy control can be found in [4], [51], [12], [57]. Some other design and analysis approaches for fuzzy controllers include cell-to-cell mapping techniques [13], [87], model-based design method =-=[98]-=-, self-organizing controllers [75], [99], and so on. As more and more people are working in this field, new design methods are coming out sooner than before. VI. Concluding Remarks A. A. Current Probl... |

146 |
Learning with localized receptive fields
- Moody, Darken
- 1988
(Show Context)
Citation Context ...field is a well-known structure that has been studied in the regions of the cerebral cortex, the visual cortex, and so forth. Drawing on the knowledge of biological receptive fields, Moody and Darken =-=[66]-=-, [67] proposed a network structure that employs local receptive fields to perform function mappings. Similar schemes have been proposed by Powell [74], Broomhead and Lowe [7], and many others in the ... |

110 | Integrating design stages of fuzzy systems using genetic algorithms”.
- Takagi, Lee
- 1993
(Show Context)
Citation Context ...[44], [45], downhill Simplex method [68], and random method [63]. In particular, use of genetic algorithms for neural network controllers can be found in [112]; for fuzzy logic controllers, see [39], =-=[52]-=-, [38]. If the plant model is not available, we can apply reinforcement learning [2] to find a working controller directly. The close relationship between reinforcement learning and dynamic programmin... |

101 |
Stable adaptive fuzzy control of nonlinear systems,”
- Wang
- 1993
(Show Context)
Citation Context ...eedback linearizable systems. The reader is referred to [86] for a more detailed treatment of this subject. Applications of this technique to neural network and fuzzy control can be found in [82] and =-=[103]-=-, respectively. 26 F. Gain Scheduling Under certain arrangements, the first-order Sugeno fuzzy model becomes a gain scheduler that switches between several sets of feedback gains. For instance, a firs... |

98 | Self-learning fuzzy controllers based on temporal back-propagation,
- Jang
- 1992
(Show Context)
Citation Context ... a wide range of areas, such as nonlinear function modeling [24], [29], time series prediction [33], [29], on-line parameter identification for control systems [29], and fuzzy controller design [26], =-=[28]-=-. In particular, GE has been using ANFIS for modeling correction factors in steel rolling mills [6]. Here we will briefly report the application of ANFIS to chaotic time series prediction [33], [29]. ... |

98 |
Learning Machines: Foundations of Trainable Pattern Classifying Systems,
- Nilsson
- 1965
(Show Context)
Citation Context ...a e \Gammax 1 + e \Gammax : Identity function: f(x) = x: When the step function (hard-limiter) is used as the activation function for a layered network, the network is often called a perceptron [78], =-=[70]-=-, as explained in example 4. For a neural network to approximate a continuous-10 0 10 -2 -1 0 1 2 (a) step function -10 0 10 -2 -1 0 1 2 (b) sigmoid function -10 0 10 -2 -1 0 1 2 (c) hyper-tangent fun... |

94 |
Fuzzy control of pH using genetic algorithms.
- Karr
- 1993
(Show Context)
Citation Context ...aling [44], [45], downhill Simplex method [68], and random method [63]. In particular, use of genetic algorithms for neural network controllers can be found in [112]; for fuzzy logic controllers, see =-=[39]-=-, [52], [38]. If the plant model is not available, we can apply reinforcement learning [2] to find a working controller directly. The close relationship between reinforcement learning and dynamic prog... |

92 | Neural Networks for Self Learning Control Systems,"
- Nguyen, Widrow
- 1990
(Show Context)
Citation Context ...n of , a compromise between trajectory error and control efforts can be obtained. Use of back-propagation through time to train a neural network for backing up a tractor-trailer system is reported in =-=[69]-=-. The same technique was used to design an ANFIS controller for balancing an inverted pendulum [28]. Note that back-propagation through time is usually an off-line learning algorithms in the sense tha... |

88 |
A Linguistic self-organizing process controller.
- Procyk, Mamdani
- 1979
(Show Context)
Citation Context ... [4], [51], [12], [57]. Some other design and analysis approaches for fuzzy controllers include cell-to-cell mapping techniques [13], [87], model-based design method [98], self-organizing controllers =-=[75]-=-, [99], and so on. As more and more people are working in this field, new design methods are coming out sooner than before. VI. Concluding Remarks A. A. Current Problems and Possible Solutions A typic... |

85 |
Training multilayer perceptrons with the Extended Kalman Algorithm,”
- Singhal, Wu
- 1989
(Show Context)
Citation Context ... are linearized with respect to its parameters, and then the extended Kalman filter algorithm [21] is employed to update all parameters. This method has been proposed in the neural network literature =-=[85]-=-, [84], [83]. The choice of one of the above methods should be based on a trade-off between computational complexity and performance. Moreover, the whole concept of fitting data to parameterized model... |

73 | A multilayered neural network controller,"
- Psaltis, Sideris, et al.
- 1988
(Show Context)
Citation Context ...he inverse control scheme is that we are minimizing the network error instead of the overall system error. An alternative is to minimize the system error directly; this is called specialized learning =-=[76]-=-. In order to back-propagate error signals through the plant block in Figure 43, we need to find a model representing 24 the behavior of the plant. In fact, in order to apply backpropagation learning,... |

72 |
Fuzzy expert systems,
- Kandel
- 1992
(Show Context)
Citation Context ...analysis, expert systems, and computer vision. Because of its multi-disciplinary nature, the fuzzy inference system is known by a number of names, such as fuzzy-rule-based system, fuzzy expert system =-=[37]-=-, fuzzy model [97], [90], fuzzy associative memory [47], fuzzy logic controller [60], [49], [50], and simply (and ambiguously) fuzzy system. The basic structure of a fuzzy inference system consists of... |

59 |
An approach to fuzzy reasoning method,
- Tsukamoto
- 1979
(Show Context)
Citation Context ... this simplification could lead to the loss of MF linguistic meanings unless the sum of firing strengths (that is, P i w i ) is close to unity. D.3 Tsukamoto Fuzzy Model In the Tsukamoto fuzzy models =-=[100]-=-, the consequent of each fuzzy if-then rule is represented by a fuzzy set with a monotonical MF, as shown in Figure 16. As a result, the inferred output of each rule is defined as a crisp value induce... |

50 |
Reinforcement Structure/Parameter Learning for Neural-Network- Based Fuzzy Logic Control Systems",
- Ling, Lee
(Show Context)
Citation Context ...forcement learning includes temporal difference methods (TD() algorithms) and Q-learning [107]. Representative applications of reinforcement learning to fuzzy control can be found in [4], [51], [12], =-=[57]-=-. Some other design and analysis approaches for fuzzy controllers include cell-to-cell mapping techniques [13], [87], model-based design method [98], self-organizing controllers [75], [99], and so on.... |

48 |
Fuzzy modeling using generalized neural networks and Kalman filter algorithm,"
- Jang
- 1991
(Show Context)
Citation Context ...nsformation is linear in some of the network's parameters, then we can identify these linear parameters by the well-known linear least-squares method. This observation leads to a hybrid learning rule =-=[24]-=-, [29] which combines the gradient method and the least-squares estimator (LSE) for fast identification of parameters. D.1 Off-Line Learning (Batch Learning) For simplicity, assume that the adaptive n... |

42 |
Computer-Oriented Approaches to Pattern Recognition”.
- Meisel
- 1972
(Show Context)
Citation Context ...with perfect plant models, we can always use gradient-free optimization schemes, such as genetic algorithms [22], [19], simulated annealing [44], [45], downhill Simplex method [68], and random method =-=[63]-=-. In particular, use of genetic algorithms for neural network controllers can be found in [112]; for fuzzy logic controllers, see [39], [52], [38]. If the plant model is not available, we can apply re... |

41 |
Neural Fuzzy Control Systems with structure and Parameter Learning, World Scientific Publishing,
- Lin
- 1994
(Show Context)
Citation Context ...and the number of fuzzy if-then rules, and so on, is now an active research topic in the field. Work along this direction includes Jang's fuzzy CART approach [30], Lin's reinforcement learning method =-=[55]-=-, Sun's fuzzy k-d trees [92], Sugeno's iterative method [91] and various clustering algorithms proposed by Chiu [15], Khedkar [43] and Wang [104]. Moreover, advances on the constructive and destructiv... |

41 |
Optimal Algorithms for Adaptive Networks: Second-Order Backpropagation, SecondOrder Direct Propagation, and Second-Order Hebbian Learning,"
- Parker
- 1987
(Show Context)
Citation Context ...better learning algorithms hold equally true for both neural networks and fuzzy models. Variants of gradient descent proposed in the neural network literature; including second-order back-propagation =-=[72]-=-, quickpropagation [17], and so on, can be used to speed up training. A number of techniques used in nonlinear regression can also contribute in this regard, such as the GuassNewton method (linearizat... |

37 |
Adaptive equalization of finite nonlinear channels using multilayer perceptrons
- Chen, Gibson, et al.
- 1990
(Show Context)
Citation Context ...capability, the applications to adaptive signal processing and control are expected. Potential applications within adaptive signal processing in27 cludes adaptive filtering [21], channel equalization =-=[9]-=-, [10], [106], noise or echo cancelling [111], predictive coding [53], and so on. Acknowledgments The authors wish to thank Steve Chiu for providing numerous helpful comments. Most of this paper was f... |

37 |
Exploiting Neurons with Localized Receptive Fields to Learn Chaos
- Stokbro, Umberger, et al.
- 1990
(Show Context)
Citation Context ...field; that is, f i is a linear function of the input variables instead of a constant: f i = ~a i \Delta ~x + b i ; (51) where ~a i is a parameter vector and b i is a scalar parameter. Stokbro et al. =-=[88]-=- used this structure to model the MackeyGlass chaotic time series [59] and found that this extended version performed better than the original RBFN with the same number of fitting parameters. It was p... |

36 | Fast learning in multi-resolution hierarchies
- Moody
- 1989
(Show Context)
Citation Context ... (59) The prediction of future values of this time series is a benchmark problem that has been used and reported by a number of connectionist researchers, such as Lapedes and Farber [48], Moody [67], =-=[65]-=-, Jones et al. [35], Crower [77], and Sanger [81]. The simulation results presented here were reported in [33], [29]; more details can be found therein. The goal of the task is to use past values of t... |

33 |
A tree-structured adaptive network for function approximation in high-dimensional spaces
- Sanger
- 1991
(Show Context)
Citation Context ...e series is a benchmark problem that has been used and reported by a number of connectionist researchers, such as Lapedes and Farber [48], Moody [67], [65], Jones et al. [35], Crower [77], and Sanger =-=[81]-=-. The simulation results presented here were reported in [33], [29]; more details can be found therein. The goal of the task is to use past values of the time series up to the point x = t to predict t... |

33 |
Optimal Filtering Algorithms for Fast Learning in Feed-Forward Neural Networks,"
- Shah, Palmeiri, et al.
- 1992
(Show Context)
Citation Context ...zed with respect to its parameters, and then the extended Kalman filter algorithm [21] is employed to update all parameters. This method has been proposed in the neural network literature [85], [84], =-=[83]-=-. The choice of one of the above methods should be based on a trade-off between computational complexity and performance. Moreover, the whole concept of fitting data to parameterized models is called ... |

31 | Use of rule-based system for process control,
- Bernard
- 1988
(Show Context)
Citation Context ...information plus trial-and-error tuning includes steam engine and boiler control [60], Sendai subway systems [116], container ship crane control [115], elevator control [54], nuclear reaction control =-=[5]-=-, automobile transmission control [40], aircraft control [14], and many others [89]. With the availability of learning algorithms, a wider range of applications is expected. Note that this approach is... |

30 |
Reconstruction of binary signals using an adaptive radial-basis-function equalizer
- Chen, Gibson, et al.
- 1991
(Show Context)
Citation Context ...ility, the applications to adaptive signal processing and control are expected. Potential applications within adaptive signal processing in27 cludes adaptive filtering [21], channel equalization [9], =-=[10]-=-, [106], noise or echo cancelling [111], predictive coding [53], and so on. Acknowledgments The authors wish to thank Steve Chiu for providing numerous helpful comments. Most of this paper was finishe... |

28 |
A defuzzification strategy for a fuzzy logic controller employing prohibitive information in command formulation.
- Pfluger, Yen, et al.
- 1992
(Show Context)
Citation Context ...hese defuzzification methods are computation intensive and there is no rigorous way to analyze them except through experimentbased studies. Other more flexible defuzzification methods can be found in =-=[73]-=-, [114], [80]. Both Figure 12 and 13 conform to the fuzzy reasoning defined previously. In practice, however, a fuzzy inference system may have certain reasoning mechanisms that do not follow the stri... |

27 |
Feedback Theory - Further Properties of Signal Flow Graphs,"
- Mason
- 1956
(Show Context)
Citation Context ...ying equation (31) may be hard to find. Here we shall not go into details about continuously operated networks. A detailed treatment of continuously operated networks which use the Mason gain formula =-=[62]-=- as a learning rule can be found in [34]. On the other hand, if a network is operated synchronously, all nodes change their outputs simultaneously according to a global clock signal and there is a tim... |

25 |
A neuro-fuzzy classifier and its applications
- Jang, Sun
(Show Context)
Citation Context ...cific application. By employing the adaptive network as a common framework, we have also proposed other adaptive fuzzy models tailored for different purposes, such as the neuro-fuzzy classifier [93], =-=[94]-=- for data classification and the fuzzy filter scheme [95], [96] for feature extraction. There are a number of possible extensions and applications and they are currently under investigation. During th... |

21 | Structure determination in fuzzy modelling: A fuzzy cart approach
- Jang
- 1994
(Show Context)
Citation Context ...style, the number of MF's for each input, and the number of fuzzy if-then rules, and so on, is now an active research topic in the field. Work along this direction includes Jang's fuzzy CART approach =-=[30]-=-, Lin's reinforcement learning method [55], Sun's fuzzy k-d trees [92], Sugeno's iterative method [91] and various clustering algorithms proposed by Chiu [15], Khedkar [43] and Wang [104]. Moreover, a... |

21 |
Function approximation and time series prediction with neural networks
- Jones, Lee, et al.
- 1990
(Show Context)
Citation Context ...n of future values of this time series is a benchmark problem that has been used and reported by a number of connectionist researchers, such as Lapedes and Farber [48], Moody [67], [65], Jones et al. =-=[35]-=-, Crower [77], and Sanger [81]. The simulation results presented here were reported in [33], [29]; more details can be found therein. The goal of the task is to use past values of the time series up t... |

20 |
A self-learning rule-based controller employing approximate reasoning and neural net concepts
- Lee
- 1991
(Show Context)
Citation Context ...ants of reinforcement learning includes temporal difference methods (TD() algorithms) and Q-learning [107]. Representative applications of reinforcement learning to fuzzy control can be found in [4], =-=[51]-=-, [12], [57]. Some other design and analysis approaches for fuzzy controllers include cell-to-cell mapping techniques [13], [87], model-based design method [98], self-organizing controllers [75], [99]... |

18 |
Industrial applications of fuzzy logic at general electric
- Bonissone, Badami, et al.
- 1995
(Show Context)
Citation Context ... [29], on-line parameter identification for control systems [29], and fuzzy controller design [26], [28]. In particular, GE has been using ANFIS for modeling correction factors in steel rolling mills =-=[6]-=-. Here we will briefly report the application of ANFIS to chaotic time series prediction [33], [29]. The time series used in our simulation is generated by the Mackey-Glass differential delay equation... |

18 |
System identification: least-squares methods,”
- Hsia
- 1977
(Show Context)
Citation Context ... : ` = (A T A) \Gamma1 A T B; (42) where A T is the transpose of A and (A T A) \Gamma1 A T is the pseudo-inverse of A if A T A is non-singular. Of course, we can also employ the recursive LSE formula =-=[23]-=-, [1], [58]. Specifically, let the i-th row vector of matrix A defined in equation (41) be a T i and the i-th element of B be b T i ; then ` can be calculated iteratively as follows: ` i+1 = ` i + S i... |

15 |
Controller Design Without Domain Experts
- Jang
(Show Context)
Citation Context ...approximate Jacobian matrix to achieve the same learning effects can be found in [41], [11], [102]. Applying specialized learning to find an ANFIS controller for the inverted pendulum was reported in =-=[27]-=-. desired model + - e x x (k+1) d + - e x x (k+1) d controller ANFIS plant x(k) x(k+1) u(k) controller ANFIS plant x(k) x(k+1) u(k) (a) (b) Fig. 43. Block diagram for (a) specialized learning; (b) spe... |

15 |
Structure Level Adaptation for Artificial Neural Networks,
- Lee
- 1991
(Show Context)
Citation Context ...'s iterative method [91] and various clustering algorithms proposed by Chiu [15], Khedkar [43] and Wang [104]. Moreover, advances on the constructive and destructive learning of neural networks [18], =-=[53]-=- can also shed some lights on this problem. Though we can speed up the parameter identification problem by introducing the least-squares estimator into the learning cycle, gradient descent still slows... |

13 |
Learning control with neural networks
- Chen, Pao
- 1989
(Show Context)
Citation Context ... the plant's inputs and outputs during two consecutive time instants. Other similar methods that aim at using an approximate Jacobian matrix to achieve the same learning effects can be found in [41], =-=[11]-=-, [102]. Applying specialized learning to find an ANFIS controller for the inverted pendulum was reported in [27]. desired model + - e x x (k+1) d + - e x x (k+1) d controller ANFIS plant x(k) x(k+1) ... |

13 |
The Fuzzy Logic Toolbox for use with MATLAB”: The MathWorks Inc.,
- Jang, Gulley
- 1995
(Show Context)
Citation Context ... desired control actions to a fuzzy controller. Examples of applying this method to both one-pole and two-pole inverted pendulum systems with varying pole lengths can be found in the demo programs in =-=[31]-=-. G. Others Other design techniques that do not use the learning algorithm in neuro-fuzzy modeling are summarized here. For complex control problems with perfect plant models, we can always use gradie... |

13 |
Predicting chaotic time series with fuzzy if then rules
- Jang
- 1993
(Show Context)
Citation Context ...th disciplines in many respects. C. Application to Chaotic Time Series Prediction ANFIS can be applied to a wide range of areas, such as nonlinear function modeling [24], [29], time series prediction =-=[33]-=-, [29], on-line parameter identification for control systems [29], and fuzzy controller design [26], [28]. In particular, GE has been using ANFIS for modeling correction factors in steel rolling mills... |

12 |
A description of the dynamical behavior of fuzzy systems
- Chen, Tsao
- 1989
(Show Context)
Citation Context ... applications of reinforcement learning to fuzzy control can be found in [4], [51], [12], [57]. Some other design and analysis approaches for fuzzy controllers include cell-to-cell mapping techniques =-=[13]-=-, [87], model-based design method [98], self-organizing controllers [75], [99], and so on. As more and more people are working in this field, new design methods are coming out sooner than before. VI. ... |

12 |
Frzzy Logic for Control of Roll and Moment for a Flexible Wing Aircraft
- Chiu
- 1991
(Show Context)
Citation Context ...e and boiler control [60], Sendai subway systems [116], container ship crane control [115], elevator control [54], nuclear reaction control [5], automobile transmission control [40], aircraft control =-=[14]-=-, and many others [89]. With the availability of learning algorithms, a wider range of applications is expected. Note that this approach is not only for control applications. If the target system to b... |

12 |
MEKA - A Fast Local Algorithm for Training Feedfoward Neural Networks
- Shah, Palmieri
- 1990
(Show Context)
Citation Context ...inearized with respect to its parameters, and then the extended Kalman filter algorithm [21] is employed to update all parameters. This method has been proposed in the neural network literature [85], =-=[84]-=-, [83]. The choice of one of the above methods should be based on a trade-off between computational complexity and performance. Moreover, the whole concept of fitting data to parameterized models is c... |

10 |
Rule extraction using generalized neural networks
- Jang
- 1991
(Show Context)
Citation Context ...zy Inference Systems A class of adaptive networks that act as a fundamental framework for adaptive fuzzy inference systems is introduced in this section. This type of networks is referred to as ANFIS =-=[25]-=-, [24], [29], which stands for AdaptiveNetwork -based Fuzzy Inference System, or semantically equivalently, Adaptive Neuro-Fuzzy Inference System. We will describe primarily the ANFIS architecture and... |

10 |
Automated Calibration of a Fuzzy Logic Controller Using a Cell State Space Algorithm,"
- Smith, Comer
- 1991
(Show Context)
Citation Context ...cations of reinforcement learning to fuzzy control can be found in [4], [51], [12], [57]. Some other design and analysis approaches for fuzzy controllers include cell-to-cell mapping techniques [13], =-=[87]-=-, model-based design method [98], self-organizing controllers [75], [99], and so on. As more and more people are working in this field, new design methods are coming out sooner than before. VI. Conclu... |

9 |
Experiments with the use of a rulebased self-organizing controller for robotic applications
- Tanscheit, Scharf
- 1988
(Show Context)
Citation Context ...[51], [12], [57]. Some other design and analysis approaches for fuzzy controllers include cell-to-cell mapping techniques [13], [87], model-based design method [98], self-organizing controllers [75], =-=[99]-=-, and so on. As more and more people are working in this field, new design methods are coming out sooner than before. VI. Concluding Remarks A. A. Current Problems and Possible Solutions A typical mod... |

5 |
A self-learning fuzzy controller with application to automobile tracking problem
- Jang
- 1991
(Show Context)
Citation Context ...ied to a wide range of areas, such as nonlinear function modeling [24], [29], time series prediction [33], [29], on-line parameter identification for control systems [29], and fuzzy controller design =-=[26]-=-, [28]. In particular, GE has been using ANFIS for modeling correction factors in steel rolling mills [6]. Here we will briefly report the application of ANFIS to chaotic time series prediction [33], ... |

4 |
Electronically controlled continuously variable transmission (ECVTII
- KASAI, MORIMOTO
- 1988
(Show Context)
Citation Context ...ng includes steam engine and boiler control [60], Sendai subway systems [116], container ship crane control [115], elevator control [54], nuclear reaction control [5], automobile transmission control =-=[40]-=-, aircraft control [14], and many others [89]. With the availability of learning algorithms, a wider range of applications is expected. Note that this approach is not only for control applications. If... |

4 |
Learning as Adaptive Interpolation in Neural Fuzzy Systems
- Khedkar
- 1993
(Show Context)
Citation Context ... Jang's fuzzy CART approach [30], Lin's reinforcement learning method [55], Sun's fuzzy k-d trees [92], Sugeno's iterative method [91] and various clustering algorithms proposed by Chiu [15], Khedkar =-=[43]-=- and Wang [104]. Moreover, advances on the constructive and destructive learning of neural networks [18], [53] can also shed some lights on this problem. Though we can speed up the parameter identific... |

4 |
An improved scheme for direct adaptive control of dynamical systems using backpropagation neural networks
- Venugopal
- 1995
(Show Context)
Citation Context ...lant's inputs and outputs during two consecutive time instants. Other similar methods that aim at using an approximate Jacobian matrix to achieve the same learning effects can be found in [41], [11], =-=[102]-=-. Applying specialized learning to find an ANFIS controller for the inverted pendulum was reported in [27]. desired model + - e x x (k+1) d + - e x x (k+1) d controller ANFIS plant x(k) x(k+1) u(k) co... |

4 |
Training of fuzzy logic systems using nearest neighborhood clustering
- Wang
(Show Context)
Citation Context ...CART approach [30], Lin's reinforcement learning method [55], Sun's fuzzy k-d trees [92], Sugeno's iterative method [91] and various clustering algorithms proposed by Chiu [15], Khedkar [43] and Wang =-=[104]-=-. Moreover, advances on the constructive and destructive learning of neural networks [18], [53] can also shed some lights on this problem. Though we can speed up the parameter identification problem b... |

3 |
A self-learning fuzzy controller
- Chen, Lin, et al.
- 1992
(Show Context)
Citation Context ...f reinforcement learning includes temporal difference methods (TD() algorithms) and Q-learning [107]. Representative applications of reinforcement learning to fuzzy control can be found in [4], [51], =-=[12]-=-, [57]. Some other design and analysis approaches for fuzzy controllers include cell-to-cell mapping techniques [13], [87], model-based design method [98], self-organizing controllers [75], [99], and ... |

2 |
Characteristics of the functionallink net: A higher order delta rule net
- Klassen, Pao
- 1988
(Show Context)
Citation Context ...the dimension of the search space of the original back-propagation method. If we fix the membership functions and adapt only the consequent part, then ANFIS can be viewed as a functional-link network =-=[46], [71] where the &qu-=-ot;enhanced representations " of the input variables are obtained via the membership functions. These "enhanced representations", which take advantage of human knowledge, apparently exp... |

2 |
Crowder Predicting the Mackey-Glass timeseries with cascade-correlation learning
- S
- 1990
(Show Context)
Citation Context ...alues of this time series is a benchmark problem that has been used and reported by a number of connectionist researchers, such as Lapedes and Farber [48], Moody [67], [65], Jones et al. [35], Crower =-=[77]-=-, and Sanger [81]. The simulation results presented here were reported in [33], [29]; more details can be found therein. The goal of the task is to use past values of the time series up to the point x... |

2 |
Defuzzification and ranking in the context of membership value semantics, rule modality, and measurement theory
- Runkler, Glesner
- 1994
(Show Context)
Citation Context ...ication methods are computation intensive and there is no rigorous way to analyze them except through experimentbased studies. Other more flexible defuzzification methods can be found in [73], [114], =-=[80]-=-. Both Figure 12 and 13 conform to the fuzzy reasoning defined previously. In practice, however, a fuzzy inference system may have certain reasoning mechanisms that do not follow the strict definition... |

2 |
Rulebase structure identification in an adaptive network based fuzzy inference system
- Sun
- 1994
(Show Context)
Citation Context ...hen rules, and so on, is now an active research topic in the field. Work along this direction includes Jang's fuzzy CART approach [30], Lin's reinforcement learning method [55], Sun's fuzzy k-d trees =-=[92]-=-, Sugeno's iterative method [91] and various clustering algorithms proposed by Chiu [15], Khedkar [43] and Wang [104]. Moreover, advances on the constructive and destructive learning of neural network... |

2 |
Adaptive network based fuzzy classification
- Sun, Jang
- 1992
(Show Context)
Citation Context ... a specific application. By employing the adaptive network as a common framework, we have also proposed other adaptive fuzzy models tailored for different purposes, such as the neuro-fuzzy classifier =-=[93]-=-, [94] for data classification and the fuzzy filter scheme [95], [96] for feature extraction. There are a number of possible extensions and applications and they are currently under investigation. Dur... |

1 |
Neuro-fuzzy modeling: an computational approach to intelligence
- Jang, Sun
- 1995
(Show Context)
Citation Context ...strates these two interpretations of a fuzzy rule A ! B. Here we shall adopt the first interpretation, where A ! B implies A coupled with B. The treatment of the second interpretation can be found in =-=[34]-=-, [49], [50]. Y A B (a) X Y A B X (b) Fig. 5. Two interpretations of fuzzy implication: (a) A coupled with B; (b) A entails B.. C. Fuzzy Reasoning (Approximate Reasoning) Fuzzy reasoning (also known a... |

1 |
Hierarchical mextures of experts and the EM algorithm
- Jordan, Jacobs
- 1993
(Show Context)
Citation Context ... and results in fast convergence to good parameter values that captures the underlying dynamics. ffl ANFIS consists of fuzzy rules which are actually local mappings (which are called local experts in =-=[36]-=-) instead of global ones. These local mappings facilitate the minimal disturbance principle [110], which states that the adaptation should not only reduce the output error for the current training pat... |

1 |
GAs for fuzzy controllers
- Karr
- 1991
(Show Context)
Citation Context ...[45], downhill Simplex method [68], and random method [63]. In particular, use of genetic algorithms for neural network controllers can be found in [112]; for fuzzy logic controllers, see [39], [52], =-=[38]-=-. If the plant model is not available, we can apply reinforcement learning [2] to find a working controller directly. The close relationship between reinforcement learning and dynamic programming was ... |

1 |
The application of a neural fuzzy controller to process control
- Kelly, Burton, et al.
- 1994
(Show Context)
Citation Context ...eover, minimization of the network error jje u (k)jj 2 does not guarantee minimization of the overall system error jjx d (k) \Gamma x(k)jj 2 . Using ANFIS for adaptive inverse control can be found in =-=[42]-=-. ANFIS identifier e u x (k) d controller ANFIS plant u(k) x(k) x(k+1) + - x(k) plant x(k+1) (a) (b) u(k) Fig. 42. Block diagram for inverse control method: (a) learning phase; (b) application phase. ... |

1 |
Neural network analysis of plasma spectra
- Sun, Jang, et al.
- 1993
(Show Context)
Citation Context ... common framework, we have also proposed other adaptive fuzzy models tailored for different purposes, such as the neuro-fuzzy classifier [93], [94] for data classification and the fuzzy filter scheme =-=[95]-=-, [96] for feature extraction. There are a number of possible extensions and applications and they are currently under investigation. During the past years, we have witnessed the rapid growth of the a... |

1 |
Using fuzzy filters as feature detectors
- Sun, Shuai, et al.
- 1994
(Show Context)
Citation Context ...n framework, we have also proposed other adaptive fuzzy models tailored for different purposes, such as the neuro-fuzzy classifier [93], [94] for data classification and the fuzzy filter scheme [95], =-=[96]-=- for feature extraction. There are a number of possible extensions and applications and they are currently under investigation. During the past years, we have witnessed the rapid growth of the applica... |