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First, we consider non-linear discrete-time and continuous-time systems with unknown inputs. The problem of reconstructing an input using the information given by an output equation is investigated. Then we examine a control problem for non-linear discrete-time hereditary systems, i.e. the problem of finding a control which drives the state of the system from its initial value to a given desired final...
The study of human handwriting movements is of great interest to researchers and biologists. It can lead to an understanding of the properties of the biological system that generates the human handwriting movements. With the identification of a dynamical system that exhibits characteristics similar to the biological one, it is possible to study handwriting movements, to identify their driving motor...
In this paper, a Single-Input Single-Output (SISO) Sugeno fuzzy model of the zeroth order with Beta membership functions for input variables is adopted. After the introduction of Beta Fuzzy Logic Systems (BFLS) a constructive theory is developed to establish the fact that they are universal approximators. Based on this theory, an algorithm, which can actually construct a BFLS approximating a given...
The Abstraction Based Connectionist Analogy Processor (AB-CAP) is a trainable neural network for analogical learning/inference. An internal abstraction model, which extracts the underlying relational isomorphism and expresses predicate-argument bindings at the abstract level, is induced structurally as a result of the backpropagation training coupled with a structure- pruning mechanism. AB-CAP also...
This paper compares two different approaches to the construction of Takagi-Sugeno fuzzy models from data. These models approximate nonlinear systems by means of interpolation between local linear models. The main issue in the construction of Takagi-Sugeno models is the decomposition of the operating space into validity regions for the local models. The way this decomposition is done influences the...
A new neural network based pattern recognition algorithm is proposed. The method consists in preprocessing the multidimensional data, using a space-filling curve based transformation into the unit interval, and employing Kohonen's vector quantization algorithms (of SOM and LVQ types) in one dimension. The space-filling based transformation preserves the theoretical Bayes risk. Experiments show that...
A framework for Similarity-Based Methods (SBMs) includes many classification models as special cases: neural networks of the Radial Basis Function type, Feature Space Mapping neurofuzzy networks based on separable transfer functions, Learning Vector Quantization, variants of the k nearest neighbor methods and several new models that may be presented in a network form. Multilayer Perceptrons (MLPs)...
Several important fuzzy implications and their properties are described on the basis of an axiomatic approach to the definition of the fuzzy implications. Then the idea of approximate reasoning using the generalized modus ponens and fuzzy implications is considered. The elimination of the non-informative part of the final fuzzy set before defuzzification plays the key role in this paper. After reviewing...
The paper describes an application of regularization techniques to an automatic choice of parameters driving the learning process in the NM-Delta neural network architecture. The heterogeneous learning algorithm is identified as very similar to the Levenberg-Marquardt method but with a considerably smaller computational cost and different justification of parameter selection. The performance of the...
The study is concerned with the fundamentals of granular computing and its application to neural networks. Granular computing, as the name itself stipulates, deals with representing information in the form of some aggregates (embracing a number of individual entitites) and their ensuing processing. We elaborate on the rationale behind granular computing. Next, a number of formal frameworks of information...
This paper presents connectionist multi-layer architectures of neuro-fuzzy systems based on various fuzzy implications. The well-known Mamdani approach (constructive) and the logical approach (destructive) are considered. Two kinds of architectures, a simpler and a more general one, are distinguished. Examples of application to classification and control problems are provided.
We chronicle the research on the fusion technology of neural networks and fuzzy systems (NN+FS), the models that have been proposed from this research, and the commercial products and industrial systems that have adopted these models. First, we review the NN+FS research activity during the early stages of their development in Japan, the US, and Europe. Next, following the classifi- cation of NN+FS...
In this paper, we present basic ideas and perspectives related to the use of fuzzy logic for the derivation of linguistic summaries of data (databases). We concentrate on the issue of how to measure the goodness of a linguistic summary, and on how to embed data summarization within the fuzzy querying environment, for an effective and efficient implementation. In particular, we propose how to efficiently...
Analytic interpolation problems arise quite naturally in a variety of engineering applications. This is due to the fact that analyticity of a (transfer) function relates to the stability of a corresponding dynamical system, while positive realness and contractiveness relate to passivity. On the other hand, the degree of an interpolant relates to the dimension of the pertinent system, and this motivates...
This paper gives an overview of the formulation and solution of network equations, with emphasis on the historical development of this area. Networks are mathematical models. The three ingredients of network descriptions are discussed. It is shown how the network equations of one-dimensional multi-port networks can be formulated and solved symbolically. If necessary, the network graph is modified...
A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.
Motion planning, i.e., steering a system from one state to another, is a basic question in automatic control. For a certain class of systems described by ordinary differential equations and called flat systems (Fliess et al., 1995; 1999a), motion planning admits simple and explicit solutions. This stems from an explicit description of the trajectories by an arbitrary time function y, the flat output,...
It has been experimentally verified that most commonly used subspace methods for identification of linear state-space systems with exogenous inputs may, in certain experimental conditions, run into ill-conditioning and lead to ambiguous results. An analysis of the critical situations has lead us to propose a new algorithmic structure which could be used either to test difficult cases and/or to implement...
This contribution deals with different concepts of nonlinear control for mechatronic systems. Since most physical systems are nonlinear in nature, it is quite obvious that an improvement in the performance of the closed loop can often be achieved only by means of control techniques that take the essential nonlinearities into consideration. Nevertheless, it can be observed that industry often hesitates...
In this paper, we introduce several system theoretic problems brought forward by recent studies on neural models of motor control. We focus our attention on three topics: (i) the cerebellum and adaptive control, (ii) reinforcement learning and the basal ganglia, and (iii) modular control with multiple models. We discuss these subjects from both neuroscience and systems theory viewpoints with the aim...
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