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114
Neurofuzzy modeling and control
 IEEE Proceedings
, 1995
"... Abstract  Fundamental and advanced developments in neurofuzzy synergisms for modeling and control are reviewed. The essential part of neurofuzzy synergisms comes from a common framework called adaptive networks, which uni es both neural networks and fuzzy models. The fuzzy models under the framew ..."
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Cited by 176 (1 self)
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Abstract  Fundamental and advanced developments in neurofuzzy synergisms for modeling and control are reviewed. The essential part of neurofuzzy synergisms comes from a common framework called adaptive networks, which uni es both neural networks and fuzzy models. The fuzzy models under the framework of adaptive networks is called ANFIS (AdaptiveNetworkbased Fuzzy Inference System), which possess certain advantages over neural networks. We introduce the design methods for ANFIS in both modeling and control applications. Current problems and future directions for neurofuzzy approaches are also addressed. KeywordsFuzzy logic, neural networks, fuzzy modeling, neurofuzzy modeling, neurofuzzy control, ANFIS. I.
The Paradoxical Success of Fuzzy Logic
 IEEE Expert
, 1993
"... Applications of fuzzy logic in heuristic control have been highly successful, but which aspects of fuzzy logic are essential to its practical usefulness? This paper shows that an apparently reasonable version of fuzzy logic collapses mathematically to twovalued logic. Moreover, there are few if any ..."
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Cited by 80 (1 self)
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Applications of fuzzy logic in heuristic control have been highly successful, but which aspects of fuzzy logic are essential to its practical usefulness? This paper shows that an apparently reasonable version of fuzzy logic collapses mathematically to twovalued logic. Moreover, there are few if any published reports of expert systems in realworld use that reason about uncertainty using fuzzy logic. It appears that the limitations of fuzzy logic have not been detrimental in control applications because current fuzzy controllers are far simpler than other knowledgebased systems. In the future, the technical limitations of fuzzy logic can be expected to become important in practice, and work on fuzzy controllers will also encounter several problems of scale already known for other knowledgebased systems. 1
The local paradigm for modeling and control: from neurofuzzy . . .
, 2001
"... The composition of simple local models for approximating complex nonlinear mappings is a common practice in recent modeling and control literature. This paper presents a comparative analysis of two different local approaches: the neurofuzzy inference system and the lazy learning approach. Neurofu ..."
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Cited by 17 (7 self)
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The composition of simple local models for approximating complex nonlinear mappings is a common practice in recent modeling and control literature. This paper presents a comparative analysis of two different local approaches: the neurofuzzy inference system and the lazy learning approach. Neurofuzzy is a hybrid representation which combines the linguistic description typical of fuzzy inference systems, with learning procedures inspired by neural networks. Lazy learning is a memorybased technique that uses a querybased approach to select the best local model configuration by assessing and comparing different alternatives in crossvalidation. In this paper, the two approaches are compared both as learning algorithms, and as identification modules of an adaptive control system. We show that lazy learning is able to provide better modeling accuracy and higher control performance at the cost of a reduced readability of the resulting approximator. Illustrative examples of identi cation and control of a nonlinear system starting from simulated data are given.
The Uses of Fuzzy Logic in Autonomous Robot Navigation: a Catalogue Raisonné
, 1997
"... The development of techniques for autonomous navigation in realworld environments constitutes one of the major trends in the current research on robotics. An important problem in autonomous navigation is the need to cope with the large amount of uncertainty that is inherent of natural environmen ..."
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Cited by 17 (1 self)
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The development of techniques for autonomous navigation in realworld environments constitutes one of the major trends in the current research on robotics. An important problem in autonomous navigation is the need to cope with the large amount of uncertainty that is inherent of natural environments. Fuzzy logic has features that make it an adequate tool to address this problem. In this paper, we review some of the possible uses of fuzzy logic in the field of autonomous navigation. We focus on four issues: how to design robust behaviorproducing modules; how to coordinate the activity of several such modules; how to use data from the sensors; and how to integrate highlevel reasoning and lowlevel execution. For each issue, we review some of the proposals in the literature, and discuss the pros and cons of fuzzy logic solutions.
Lazy Learning for Local Modeling and Control Design
 INTERNATIONAL JOURNAL OF CONTROL. ACCEPTED
, 1997
"... This paper presents local methods for modeling and control of discretetime unknown nonlinear dynamical systems, when only a limited amount of inputoutput data is available. We propose the adoption of lazy learning, a memorybased technique for local modeling. The modeling procedure uses a queryba ..."
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Cited by 12 (4 self)
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This paper presents local methods for modeling and control of discretetime unknown nonlinear dynamical systems, when only a limited amount of inputoutput data is available. We propose the adoption of lazy learning, a memorybased technique for local modeling. The modeling procedure uses a querybased approach to select the best model configuration by assessing and comparing different alternatives. A new recursive technique for local model identification and validation is presented, together with an enhanced statistical method for model selection. Also, three methods to design controllers based on the local linearization provided by the lazy learning algorithm are described. In the first method the lazy technique returns the forward and inverse models of the system which are used to compute the control action to take. The second is an indirect method inspired to selftuning regulators where recursive least squares estimation is replaced by a local approximator. The third method combin...
Transparent Fuzzy Systems: Modeling and Control
, 2002
"... During the last twenty years, fuzzy logic has been successfully applied to many modeling and control problems. One of the reasons of success is that fuzzy logic provides humanfriendly and understandable knowledge representation that can be utilized in expert knowledge extraction and implementation. ..."
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Cited by 10 (4 self)
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During the last twenty years, fuzzy logic has been successfully applied to many modeling and control problems. One of the reasons of success is that fuzzy logic provides humanfriendly and understandable knowledge representation that can be utilized in expert knowledge extraction and implementation. It is observed, however, that transparency, which is vital for undistorted information transfer, is not a default property of fuzzy systems, moreover, application of algorithms that identify fuzzy systems from data will most likely destroy any semantics a fuzzy system ever had after initialization. This thesis thoroughly investigates the issues related to transparency. Fuzzy systems are generally divided into two classes. It is shown here that for these classes different definitions of transparency apply. For standard fuzzy systems that use fuzzy propositions in IFTHEN rules, explicit transparency constraints have been derived. Based on these constraints, exploitation/modification schemes of existing identification algorithms are suggested, moreover, a new algorithm for training standard fuzzy systems has been proposed, with a considerable potential to reduce the gap between accuracy and transparency in fuzzy modeling. For 1st order TakagiSugeno systems that are interpreted in terms of local linear models, such conditions cannot be derived due to system architecture and its undesirable interpolation properties of 1st order TS systems. It is, however, possible to solve the transparency preservation problem in the context of modeling with another proposed method that benefits from rule activation degree exponents. 1st order TS systems that admit valid interpretation of local models as linearizations of the modeled system are useful, for example, in gainscheduled control. Transparent standard fuzzy systems, on the other hand, are vital to this branch of intelligent control that seeks solutions by emulating the mechanisms of reasoning and decision processes of human beings not limited to knowledgebased fuzzy control. Performing the local inversion of the modeled system it is possible to extract relevant control information, which is demonstrated with the application of fedbatch fermentation. The more a fuzzy controller resembles the experts role in a control task, the higher will be the implementation benefit of the fuzzy engine. For example, a hierarchy of fuzzy (and nonfuzzy) controllers simulates an existing hierarchy in the human decision process and leads to improved control performance. Another benefit from hierarchy is that it assumes problem decomposition. This is especially important with fuzzy logic where large number of system variables leads to exponential explosion of rules (curse of dimensionality) that makes controller design extremely difficult or even impossible. The advantages of hierarchical control are illustrated with truck backerupper applications.
An LMI Approach for Stability Analysis of Nonlinear Systems
 in Proc. of European Control Conference
, 1997
"... This paper presents a constructive method for showing stability of nonlinear systems consisting of statedependent weighted linear systems. This kind of system representation is common in for instance fuzzy systems or when local linear models of a nonlinear system are weighted together. Stability is ..."
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Cited by 8 (2 self)
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This paper presents a constructive method for showing stability of nonlinear systems consisting of statedependent weighted linear systems. This kind of system representation is common in for instance fuzzy systems or when local linear models of a nonlinear system are weighted together. Stability is shown by joining multiple local quadratic Lyapunov functions properly in the state space. The stability conditions are formulated as a linear matrix inequality (LMI) problem. Hence, these can be verified efficiently by computerized methods. 1 Introduction In this paper we present a constructive method for showing stability of nonlinear systems consisting of statedependent weighted linear systems. A large class of nonlinear systems are represented in this way, e.g. fuzzy systems [11, 12] or weighted linearized systems [5]. The second kind of systems is the result of a linearization around several states, which gives a number of linear systems. However, contrary to approaches that approxima...
Exact TradeOff Between Approximation Accuracy and Interpretability: Solving . . .
"... Although, in literature various results can be found claiming that fuzzy rulebased systems (FRBSs) possess the universal approximation property, to reach arbitrary accuracy the necessary number of rules are unbounded. Therefore, the inherent property of FRBSs in the original sense of Zadeh, namely ..."
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Cited by 8 (4 self)
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Although, in literature various results can be found claiming that fuzzy rulebased systems (FRBSs) possess the universal approximation property, to reach arbitrary accuracy the necessary number of rules are unbounded. Therefore, the inherent property of FRBSs in the original sense of Zadeh, namely that they can be characterized by a semantic relying on linguistic terms is lost. If we restrict the number of rules, universal approximation is not valid anymore as it was shown for, including others, Sugeno and TSK type models [10,19]. Due to this theoretic bound there is recently a great demand among researchers on finding tradeoff techniques between a required accuracy and the number of rules, and as such, they attempt to determine the (optimal) number of rules as a function of accuracy. Naturally, to obtain such results one has to restrict somehow the set of continuous functions, usually requiring some smoothness conditions on the approximated function. In terms of approximation theory this is the socalled saturation problem, the determination of optimal order and class of approximation. Hitherto, saturation classes and orders have not been determined for FRBSs and neural networks. In this paper we solve the saturation problem for a special type of fuzzy controller, for the generalized KHinterpolator, being a suitable inference method in sparse rule bases.
Global Stability of Generalized Additive Fuzzy Systems
 IEEE Trans. Systems, Man, and Cybernetics  C
, 1998
"... This paper explores the stability of a class of feedback fuzzy systems. The class consists of generalized additive fuzzy systems that compute a system output as a convex sum of linear operators. Continuous versions of these systems are globally asymptotically stable if all rule matrices are stable ( ..."
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Cited by 7 (0 self)
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This paper explores the stability of a class of feedback fuzzy systems. The class consists of generalized additive fuzzy systems that compute a system output as a convex sum of linear operators. Continuous versions of these systems are globally asymptotically stable if all rule matrices are stable (negative definite). So local rule stability leads to global system stability. This relationship between local and global system stability does not hold for the better known discrete versions of feedback fuzzy systems. A corollary shows that it does hold for the discrete versions in the special but practical case of diagonal rule matrices. The paper first reviews additive fuzzy systems and then extends them to the class of generalized additive fuzzy systems. The Appendix derives the basic ratio structure of additive fuzzy systems and shows how supervised learning can tune their parameters.
Exponential Stability Analysis of Nonlinear Systems using LMIs
 In Proc. of CDC
, 1997
"... This paper presents a constructive method for showing exponential stability of autonomous nonlinear systems consisting of statedependent weighted linear systems. This kind of system representation is common in for instance fuzzy systems or is the result of an exact or approximative description of a ..."
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Cited by 7 (2 self)
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This paper presents a constructive method for showing exponential stability of autonomous nonlinear systems consisting of statedependent weighted linear systems. This kind of system representation is common in for instance fuzzy systems or is the result of an exact or approximative description of an arbitrary nonlinear vector field. Stability is shown by joining multiple local Lyapunov functions properly in the statespace. The overall Lyapunov function, consisting of the local ones, are allowed to be discontinuous at the states where the trajectory passes from one local region to another. By using local quadratic Lyapunov functions the stability conditions are formulated as linear matrix inequalities (LMIs), which can be solved efficiently by computerized methods. Keywords: Nonlinear systems, Fuzzy systems, Stability, Exponential stability, Linear matrix inequalities, LMIs 1 Introduction In this paper we present a constructive method for showing exponential stability of nonlinear sy...