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Fractional-order circuit elements with memory

Fractional-order circuit elements with memory

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International Carpathian control Conference (ICCC)

作者： 1Ivo Petráš YangQuan Chen Institute of Control and Informatization of Production Processes BERG Faculty Technical University of Košice Kosice Slovakia Department of Electrical and Computer Engineering Center for Self-Organizing and Intelligent Systems Utah State University Logan UT USA

This paper deals with the fractional-order memristive, memcapacitative, and meminductive systems and their utilization in design of the new circuits with memory. We provide a mathematical description of such systems by using a technique of the fractional calculus. Some possible applications of “mem” systems are mentioned in article as well.

关键词： Memristors Capacitors Inductors Fractional calculus Equations

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Comparison of standard and sparse-based implementation of GOSCL algorithm

Comparison of standard and sparse-based implementation of GO...

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International Symposium on Computational Intelligence and Informatics

作者： P. Butka J. Pócsová J. Pócs Department of Cybernetics and Artificial Intelligence Faculty of Electrical Engineering and Informatics Technical University of Košice Kosice Slovakia Institute of Control and Informatization of Production Processes BERG Faculty Technical University of Košice Kosice Slovakia Mathematical Institute Slovak Academy of Sciences Kosice Slovakia

ISBN: (纸本)9781467352055

In this paper we provide experimental comparison on time complexity of algorithm for creation of Generalized One-Sided Concept Lattices according to the sparseness of the input data table between standard and sparse-based implementation. It is an incremental algorithm related to FCA (Formal Concept Analysis), which is ready to be used with various attribute types and to create so-called generalized one-sided concept lattice. While these algorithms are generally exponential, in practice the complexity can be considerably reduced, e.g., for sparse input data tables. We describe sparse-based implementation of two crucial operations in our algorithm and provide experiments with different sparse data tables, where time complexity is studied for comparison of standard and sparse-based implementation of the algorithm.

关键词： comparison implementation operations Concept Lattice algorithms complexity classes Surgery incoming data Complexity

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On generation of one-sided concept lattices from restricted context

On generation of one-sided concept lattices from restricted ...

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International Symposium on Intelligent Systems and Informatics (SISY)

作者： Peter Butka Jana Pócsová Jozef Pócs Department of Cybernetics and Artificial Intelligence Faculty of Electrical Engineering and Informatics Technical University of Košice Kosice Slovakia Institute of Control and Informatization of Production Processes BERG Faculty Technical University of Košice Kosice Slovakia Mathematical Institute Slovak Academy of Sciences Kosice Slovakia

In this paper the relationship between one-sided concept lattices and their restricted version is described. One-sided concept lattices are based on the Galois connections within Formal Concept Analysis (FCA) framework, which allows to analyse object-attribute models with different structures for truth values of attributes. We present the approach for generation of one-sided concept lattices from restricted formal context, which is obtained from given one by omitting some subset of the set of all attributes. The resulted algorithm for such restricted problem is described, together with the discussion on its correctness.

关键词： Lattices Context Informatics Complexity theory Computational intelligence Algorithm design and analysis Data mining

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Cloud computing as a platform for distributed fuzzy FCA approach in data analysis

Cloud computing as a platform for distributed fuzzy FCA appr...

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IEEE International Conference on Intelligent Engineering Systems (INES)

作者： M. Sarnovský P. Butka J. Pócsová Faculty of Electrical Engineering and Informatics Department of Cybernetics and Artificial Intelligence Technical University of Košice Kosice Slovakia Faculty of Economics Technical University of Košice Kosice Slovakia BERG Faculty Institute of Control and Informatization of Production Processes Technical University of Košice Kosice Slovakia

In this paper we describe use of cloud computing platform for support of distributed creation of conceptual models based on the FCA (Formal Concept Analysis) framework. FCA is one of the approaches which can be applied in process of conceptual data analysis. Extension of classical FCA (binary table data) is (one-sided) fuzzy version that works with different types of lattice-based attributes (binary, ordinal, interval-based, etc.) in the object-attribute table. This extension, so-called generalized one-sided concept lattices, provide possibility for researcher or data analyzer to use fuzzy FCA for object-attribute tables without the need for specific unified pre-processing, what is usually expected in practical data mining or online analytical tools. Computational complexity of creation of concept lattices from large contexts (data tables) is considerable, also interpretability of huge concept lattices is problematic. Therefore, we will also propose a solution for creation of simple hierarchy of smaller FCA models. Starting data table is decomposed into smaller sets of objects and then one concept lattice is built for every subset using generalized one-sided concept lattice. Such small FCA-based models are better for interpretability, and also can be combined into one hierarchy of models using simple hierarchical clustering based on the descriptions of particular models (as weighted vectors of attributes), which can be searched in analytical tool by data analyst. Cloud infrastructure is then used for increase of computational effectiveness, because particular models are built in parallel/distributed way. This cloud module can be a part of more complex data analytical system, which is also presented at the end of the paper.

关键词： Lattices Cloud computing Computational modeling Data analysis Clustering algorithms Algorithm design and analysis Analytical models

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Comparison of the electronic realization of the fractional-order system and its model

Comparison of the electronic realization of the fractional-o...

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International Carpathian control Conference (ICCC)

作者： L'ubomír Dorčák Ján Terpák Ivo Petráš Juraj Valsa Emmanuel Gonzalez Institute of Control and Informatization of Production Processes Faculty BERG Technical University of Košice Košice Slovakia Faculty of Electrical Engineering and Computer Science Brno University of Technology Brno Czech Republic Department of Computer Technology College of Computer Studies De La Salle University Manila Philippines

Real objects in general are fractional-order (FO) systems, although in some types of systems the order is very close to an integer order. Also application of FO models is more adequate for the description of dynamical systems than integer-order models. This paper is devoted to the analogue electronic realization of the FO systems, e.g. controlled objects and/or controllers whose mathematical models are FO differential equations. The electronic realization is based on FO differentiator and FO integrator where operational amplifiers are connected with appropriate impedance or in our realization with so called Fractional Order Element (FOE) or Constant Phase Element (CPE). Presented network model in spite of its simplicity approximates quite well the properties of the ideal FO system compared with e.g. domino ladder networks. Also presented, along with the mathematical description, are simulation and measurement results.

关键词： control systems Mathematical model Transfer functions Feedback control Impedance Educational institutions

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Modeling and identification of fractional-order dynamical systems

Modeling and identification of fractional-order dynamical sy...

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11th International Multidisciplinary Scientific Geoconference and EXPO, SGEM 2011

作者： Dorčák, Ľubomír Valsa, Juraj Terpák, Ján Horovčák, Pavel Gonzalez, Emmanuel Process Control and Geotechnology Institute of Control and Informatization of Production Processes Technical University of Košice Slovakia Brno University of Technology Czech Republic Department of Computer Technology College of Computer Studies De La Salle University Manila Philippines

One of the most characteristic features of the processes in the area of mining and processing of earth resources is their complexity. The modern methods of investigation, monitoring and control of these processes utilize approaches based upon modeling of the processes. In this paper we will focus only on the dynamical processes, where the mathematical models are differential equations. As it results from the last research works, majority of the real objects in general are fractional-order systems. Fractionalorder models are more adequate for the description of dynamical systems than integerorder models. But appropriate methods for the numerical calculations of fractional-order differential equations are needed in such cases and also methods for the identification of such systems. In this contribution we describe and compare some previous methods used for simulation purposes with the methods based on approximate formulas for numerical inversion of Laplace transforms. The verification and comparison will be based mainly on the accuracy and computing time. Also an experimental method of identification is given. The verification of identification method was performed on systems with known parameters. © SGEM2011 All Rights Reserved by the International Multidisciplinary Scientific GeoConference SGEM.

关键词： Differential equations

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Comparison of the methods for the calculation of fractional-order differential equations

Comparison of the methods for the calculation of fractional-...

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2011 12th International Carpathian control Conference, ICCC'2011

作者： Dorčák, L'ubomír Valsa, Juraj Terpák, Ján Gonzalez, Emmanuel Institute of Control and Informatization of Production Processes Faculty BERG Technical University of Košice B. Němcovej 3 042 00 Košice Slovakia Faculty of Electrical Engineering and Computer Science Brno University of Technology Kolejní 2906/4 612 00 Brno Czech Republic Department of Computer Technology College of Computer Studies De La Salle University Manila Philippines

ISBN: (纸本)9781612843599

Real objects in general are fractional-order systems, although in some types of systems the order is very close to an integer order. Since major advances have been made in this area in the last decades, it is possible to consider also the real order of the dynamical systems by using fractional order of the differential equations. Such models are more adequate for the description of dynamical systems than integer-order models. Appropriate methods for the numerical calculations of fractional-order differential equations are needed. In this contribution we will compare some previous methods used for simulation purposes with the methods based on approximate formulas for numerical inversion of Laplace transforms. The verification and comparison will be based mainly on the accuracy and computing time which is very important e.g. in the tasks of simulation or identification using optimization methods where too many calculations are needed and faster methods can save time very significantly. © 2011 IEEE.

关键词： Differential equations

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Comparison of the methods for the calculation of fractional-order differential equations

Comparison of the methods for the calculation of fractional-...

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International Carpathian control Conference (ICCC)

作者： Eubomír Dorcák Juraj Valsa Ján Terpák Emmanuel Gonzalez Institute of Control and Informatization of Production Processes Faculty BERG Technical University of Košice Kosice Slovakia Faculty of Electrical Engineering and Computer Science Brno University of Technology Brno Czech Republic Department of Computer Technology College of Computer Studies De La Salle University Manila Philippines

关键词： Approximation methods Numerical models Accuracy Mathematical model Differential equations Computational modeling control systems

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Fractional-order memristive systems

Fractional-order memristive systems

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International Conference on Emerging Technologies and Factory Automation (ETFA)

作者： Ivo Petráš YangQuan Chen Calvin Coopmans Institute of Control and Informatization of Production Processes BERG Faculty Technical University of Košice Kosice Slovakia Center for Self-Organizing and Intelligent Systems (CSOIS) Electrical and Computer Engineering Department Utah State University Logan UT USA

This paper deals with the concept of (integer-order) memristive systems, which are generalized to non-integer order case using fractional calculus. We consider the memory effect of the fractional inductor (fractductor), fractional capacitor and fractional memristor. We also show that the memory effect of such devices can be also used for an analogue implementation of the fractional-order operator, namely fractional-order integral and fractional-order derivatives. This kind of operator is useful for realization of the fractional-order controllers. We present theoretical description of such implementation and we proposed the practical realization and did some simulations and experimental measurements as well.

关键词： Memristors Fractional calculus Inductors Capacitors Voltage Circuit simulation Resistors Temperature Phase change memory control systems

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Fractional Order control - A Tutorial

Fractional Order Control - A Tutorial

引用

2009 American control Conference (ACC 2009)

作者： YangQuan Chen Ivo Petras Dingyu Xue Center for Self-Organizing and Intelligent Systems (CSOIS) Department of Electrical and Computer Engineering Utah State University 4120 Old Main Hill Logan UT 84322-4120 USA Institute of Control and Informatization of Production Processes BERG Faculty Technical University of Kosice B. Nemcovej 3 042 00 Kosice Slovak Republic Faculty of Information Sciences and Engineering Northeastern University Shenyang 110004 P R China

ISBN: (纸本)9781424445233

Many real dynamic systems are better characterized using a non-integer order dynamic model based on fractional calculus or, differentiation or integration of non-integer order. Traditional calculus is based on integer order differentiation and integration. The concept of fractional calculus has tremendous potential to change the way we see, model, and control the nature around us. Denying fractional derivatives is like saying that zero, fractional, or irrational numbers do not exist. In this paper, we offer a tutorial on fractional calculus in controls. Basic definitions of fractional calculus, fractional order dynamic systems and controls are presented first. Then, fractional order PID controllers are introduced which may make fractional order controllers ubiquitous in industry. Additionally, several typical known fractional order controllers are introduced and commented. Numerical methods for simulating fractional order systems are given in detail so that a beginner can get started quickly. Discretization techniques for fractional order operators are introduced in some details too. Both digital and analog realization methods of fractional order operators are introduced. Finally, remarks on future research efforts in fractional order control are given.

关键词： Tutorial Fractional calculus control systems Three-term control Electrical equipment industry Industrial control Numerical simulation Voltage Propagation losses Transmission line theory

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