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351
ANFIS: AdaptiveNetworkBased Fuzzy Inference System
, 1993
"... This paper presents the architecture and learning procedure underlying ANFIS (AdaptiveNetwork based Fuzzy Inference System), a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an inputoutput mapping bas ..."
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Cited by 432 (5 self)
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This paper presents the architecture and learning procedure underlying ANFIS (AdaptiveNetwork based Fuzzy Inference System), a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an inputoutput mapping based on both human knowledge (in the form of fuzzy ifthen rules) and stipulated inputoutput data pairs. In our simulation, we employ the ANFIS architecture to model nonlinear functions, identify nonlinear components onlinely in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificail neural networks and earlier work on fuzzy modeling are listed and discussed. Other extensions of the proposed ANFIS and promising applications to automatic control and signal processing are also suggested. 1 Introduction System modeling based on conventional mathematical tools (e.g., differential equations) is not well suited for dealing with illdefine...
Forward models: Supervised learning with a distal teacher
 Cognitive Science
, 1992
"... Internal models of the environment have an important role to play in adaptive systems in general and are of particular importance for the supervised learning paradigm. In this paper we demonstrate that certain classical problems associated with the notion of the \teacher " in supervised learnin ..."
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Cited by 295 (7 self)
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Internal models of the environment have an important role to play in adaptive systems in general and are of particular importance for the supervised learning paradigm. In this paper we demonstrate that certain classical problems associated with the notion of the \teacher " in supervised learning can be solved by judicious use of learned internal models as components of the adaptive system. In particular, we show how supervised learning algorithms can be utilized in cases in which an unknown dynamical system intervenes between actions and desired outcomes. Our approach applies to any supervised learning algorithm that is capable of learning in multilayer networks.
Nonlinear BlackBox Modeling in System Identification: a Unified Overview
 Automatica
, 1995
"... A nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area with structures based on neural networks, radial basis networks, wavelet networks, hinging hyperplanes, ..."
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Cited by 136 (15 self)
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A nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area with structures based on neural networks, radial basis networks, wavelet networks, hinging hyperplanes, as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules. This paper describes all these approaches in a common framework, from a user's perspective. It focuses on what are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques. It is pointed out that the nonlinear structures can be seen as a concatenation of a mapping from observed data to a regression vector and a nonlinear mapping from the regressor space to the output space. These mappings are discussed separately. The latter mapping is usually formed as a basis function e...
Gradient calculation for dynamic recurrent neural networks: a survey
 IEEE Transactions on Neural Networks
, 1995
"... Abstract  We survey learning algorithms for recurrent neural networks with hidden units, and put the various techniques into a common framework. We discuss xedpoint learning algorithms, namely recurrent backpropagation and deterministic Boltzmann Machines, and non xedpoint algorithms, namely backp ..."
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Cited by 135 (3 self)
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Abstract  We survey learning algorithms for recurrent neural networks with hidden units, and put the various techniques into a common framework. We discuss xedpoint learning algorithms, namely recurrent backpropagation and deterministic Boltzmann Machines, and non xedpoint algorithms, namely backpropagation through time, Elman's history cuto, and Jordan's output feedback architecture. Forward propagation, an online technique that uses adjoint equations, and variations thereof, are also discussed. In many cases, the uni ed presentation leads to generalizations of various sorts. We discuss advantages and disadvantages of temporally continuous neural networks in contrast to clocked ones, continue with some \tricks of the trade" for training, using, and simulating continuous time and recurrent neural networks. We present somesimulations, and at the end, address issues of computational complexity and learning speed.
Gaussian Networks for Direct Adaptive Control
 IEEE Transactions on Neural Networks
, 1991
"... A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs a network of gaussian radial ..."
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Cited by 133 (8 self)
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A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities. Under mild assumptions about the degree of smoothness exhibited by the nonlinear functions, the algorithm is proven to be globally stable, with tracking errors converging to a neighborhood of zero. A constructive procedure is detailed, which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy. A stable weight adjustment mechanism is then determined using Lyapunov theory. The network construction and performance of the resulting controller are illustrated through simulations with example syst...
GradientBased Learning Algorithms for Recurrent Networks and Their Computational Complexity
, 1995
"... Introduction 1.1 Learning in Recurrent Networks Connectionist networks having feedback connections are interesting for a number of reasons. Biological neural networks are highly recurrently connected, and many authors have studied recurrent network models of various types of perceptual and memory pr ..."
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Cited by 115 (4 self)
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Introduction 1.1 Learning in Recurrent Networks Connectionist networks having feedback connections are interesting for a number of reasons. Biological neural networks are highly recurrently connected, and many authors have studied recurrent network models of various types of perceptual and memory processes. The general property making such networks interesting and potentially useful is that they manifest highly nonlinear dynamical behavior. One such type of dynamical behavior that has received much attention is that of settling to a fixed stable state, but probably of greater importance both biologically and from an engineering viewpoint are timevarying behaviors. Here we consider algorithms for training recurrent networks to perform temporal supervised learning tasks, in which the specification of desired behavior is in the form of specific examples of input and desired output trajectories. One example of such a task is sequence classification, where
Adaptive Critic Designs
 IEEE Transactions on Neural Networks
, 1997
"... We discuss a variety of Adaptive Critic Designs (ACDs) for neurocontrol. These are suitable for learning in noisy, nonlinear, and nonstationary environments. They have common roots as generalizations of dynamic programming for neural reinforcement learning approaches. Our discussion of these origins ..."
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Cited by 75 (10 self)
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We discuss a variety of Adaptive Critic Designs (ACDs) for neurocontrol. These are suitable for learning in noisy, nonlinear, and nonstationary environments. They have common roots as generalizations of dynamic programming for neural reinforcement learning approaches. Our discussion of these origins leads to an explanation of three design families: Heuristic Dynamic Programming (HDP), Dual Heuristic Programming (DHP), and Globalized Dual Heuristic Programming (GDHP). The main emphasis is on DHP and GDHP as advanced ACDs. We suggest two new modifications of the original GDHP design that are currently the only working implementations of GDHP. They promise to be useful for many engineering applications in the areas of optimization and optimal control. Based on one of these modifications, we present a unified approach to all ACDs. This leads to a generalized training procedure for ACDs. 1 The authors gratefully acknowledge support from the Texas Tech Center for Applied Research, Ford Moto...
Nonlinear Adaptive Inverse Control
, 1997
"... Adaptive control is seen as a two part problem, (a) control of plant dynamics, and (b) control of plant disturbance. Conventionally, one uses feedback control to treat both problems simultaneously. Tradeoffs and compromises are necessary to achieve good solutions, however. ..."
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Cited by 58 (2 self)
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Adaptive control is seen as a two part problem, (a) control of plant dynamics, and (b) control of plant disturbance. Conventionally, one uses feedback control to treat both problems simultaneously. Tradeoffs and compromises are necessary to achieve good solutions, however.
Learning longterm dependencies in NARX recurrent neural networks
, 1996
"... It has recently been shown that gradientdescent learning algorithms for recurrent neural networks can perform poorly on tasks that involve longterm dependencies, i.e. those problems for which the desired output depends on inputs presented at times far in the past. We show tht the longterm de ..."
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Cited by 46 (5 self)
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It has recently been shown that gradientdescent learning algorithms for recurrent neural networks can perform poorly on tasks that involve longterm dependencies, i.e. those problems for which the desired output depends on inputs presented at times far in the past. We show tht the longterm dependencies problem is lessened for a class of architectures called NARX recurrent neural networks, which have powerful representational capabilities. We have previously reported that gradient descent learning can be more effective in NARX networks than in recurrent neural network architectures that have "hidden states" on problems including grammatical inference and nonlinear system identification. Typically, the network converges much faster and generalizes better than other networks. The results in this paper are consistent with this phenomenon. We present some experimental results which show that NARX networks can often retain information for two to three times as long as conventi...