Functional Fractional Calculus For System Identification And Controls
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Functional Fractional Calculus For System Identification And Controls
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Author : Shantanu Das
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-26
Functional Fractional Calculus For System Identification And Controls written by Shantanu Das and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-26 with Technology & Engineering categories.
In this book, not only are mathematical abstractions discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls. The reader gets a feeling of the wide applicability of fractional calculus in the field of science and engineering. With this book, a starter can understand the concepts of this emerging field with a minimal effort and basic mathematics.
Functional Fractional Calculus
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Author : Shantanu Das
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-01
Functional Fractional Calculus written by Shantanu Das and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-01 with Technology & Engineering categories.
When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ‘ordinary’ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls. The normal physical laws like, transport theory, electrodynamics, equation of motions, elasticity, viscosity, and several others of are based on ‘ordinary’ calculus. In this book these physical laws are generalized in fractional calculus contexts; taking, heterogeneity effect in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, physics of random delay in computer network; and several others; mapping the reality of nature closely. The concept of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically with examples. The practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function is deliberated. Practical results of viscoelastic experiments, fractional order controls experiments, design of fractional controller and practical circuit synthesis for fractional order elements are elaborated in this book. The book also maps theory of classical integer order differential equations to fractional calculus contexts, and deals in details with conflicting and demanding initialization issues, required in classical techniques. The book presents a modern approach to solve the ‘solvable’ system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving ‘approximately exact’ series solutions. Historically, Sir Isaac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J.von Neumann remarked, “...the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking.” This XXI century has thus started to ‘think-exactly’ for advancement in science & technology by growing application of fractional calculus, and this century has started speaking the language which nature understands the best.
Kindergarten Of Fractional Calculus
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Author : Shantanu Das
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2020-02-18
Kindergarten Of Fractional Calculus written by Shantanu Das and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-18 with Mathematics categories.
This book presents a simplified deliberation of fractional calculus, which will appeal not only to beginners, but also to various applied science mathematicians and engineering researchers. The text develops the ideas behind this new field of mathematics, beginning at the most elementary level, before discussing its actual applications in different areas of science and engineering. This book shows that the simple, classical laws based on Newtonian calculus, which work quite well under limiting and idealized conditions, are not of much use in describing the dynamics of actual systems. As such, the application of non-Newtonian, or generalized, calculus in the governing equations, allows the order of differentiation and integration to take on non-integer values.
Non Integer Order Calculus And Its Applications
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Author : Piotr Ostalczyk
language : en
Publisher: Springer
Release Date : 2018-03-22
Non Integer Order Calculus And Its Applications written by Piotr Ostalczyk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-22 with Technology & Engineering categories.
This book focuses on fractional calculus, presenting novel advances in both the theory and applications of non-integer order systems. At the end of the twentieth century it was predicted that it would be the calculus of the twenty-first century, and that prophecy is confirmed year after year. Now this mathematical tool is successfully used in a variety of research areas, like engineering (e.g. electrical, mechanical, chemical), dynamical systems modeling, analysis and synthesis (e.g technical, biological, economical) as well as in multidisciplinary areas (e.g. biochemistry, electrochemistry).As well as the mathematical foundations the book concentrates on the technical applications of continuous-time and discrete-time fractional calculus, investigating the identification, analysis and control of electrical circuits and dynamical systems. It also presents the latest results.Although some scientific centers and scientists are skeptical and actively criticize the applicability of fractional calculus, it is worth breaking through the scientific and technological walls. Because the “fractional community” is growing rapidly there is a pressing need for the exchange of scientific results. The book includes papers presented at the 9th International Conference on Non-integer Order Calculus and Its Applications and is divided into three parts:• Mathematical foundations• Fractional systems analysis and synthesis• System modelingSeven papers discuss the mathematical foundations, twelve papers address fractional order analysis and synthesis and three focus on dynamical system modeling by the fractional order differential and difference equations. It is a useful resource for fractional calculus scientific community.
Sliding Modes After The First Decade Of The 21st Century
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Author : Leonid Fridman
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-10
Sliding Modes After The First Decade Of The 21st Century written by Leonid Fridman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-10 with Technology & Engineering categories.
The book presents the newest results of the major world research groups working in the area of Variable Structure Systems and Sliding Mode Control (VSS/SMC). The research activity of these groups is coordinated by the IEEE Technical Committee on Variable Structure Systems (VSS) and Sliding Modes (SM). The presented results include the reports of the research groups collaborating in a framework of the Unión European Union – México project of Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICyT) 93302 titled "Automatization and Monitoring of Energy Production Processes via Sliding Mode Control". The book starts with the overview of the sliding mode control concepts and algorithms that were developed and discussed in the last two decades The research papers are combined in three sections: Part I: VSS and SM Algorithms and their Analysis Part II: SMC Design Part III: Applications of VSS and SMC The book will be of interests of engineers, researchers and graduate students working in the area of the control systems design. Novel mathematical theories and engineering concepts of control systems are rigorously discussed and supported by numerous applications to practical tasks.
Fractional Dynamical Systems Methods Algorithms And Applications
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Author : Piotr Kulczycki
language : en
Publisher: Springer Nature
Release Date : 2022-01-04
Fractional Dynamical Systems Methods Algorithms And Applications written by Piotr Kulczycki and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-04 with Technology & Engineering categories.
This book presents a wide and comprehensive spectrum of issues and problems related to fractional-order dynamical systems. It is meant to be a full-fledge, comprehensive presentation of many aspects related to the broadly perceived fractional-order dynamical systems which constitute an extension of the traditional integer-order-type descriptions. This implies far-reaching consequences, both analytic and algorithmic, because—in general—properties of the traditional integer-order systems cannot be directly extended by a straightforward generalization to fractional-order systems, modeled by fractional-order differential equations involving derivatives of an non-integer order. This can be useful for describing and analyzing, for instance, anomalies in the behavior of various systems, chaotic behavior, etc. The book contains both analytic contributions with state-of-the-art and theoretical foundations, algorithmic implementation of tools and techniques, and—finally—some examples of relevant and successful practical applications.
Recent Advances In Intelligent Information Systems And Applied Mathematics
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Author : Oscar Castillo
language : en
Publisher: Springer Nature
Release Date : 2020-01-31
Recent Advances In Intelligent Information Systems And Applied Mathematics written by Oscar Castillo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-31 with Technology & Engineering categories.
This book describes the latest advances in intelligent techniques such as fuzzy logic, neural networks, and optimization algorithms, and their relevance in building intelligent information systems in combination with applied mathematics. The authors also outline the applications of these systems in areas like intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction, and optimization of complex problems. By sharing fresh ideas and identifying new targets/problems it offers young researchers and students new directions for their future research. The book is intended for readers from mathematics and computer science, in particular professors and students working on theory and applications of intelligent systems for real-world applications.
Fractional Order Signal Processing
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Author : Saptarshi Das
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-15
Fractional Order Signal Processing written by Saptarshi Das and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-15 with Technology & Engineering categories.
The book tries to briefly introduce the diverse literatures in the field of fractional order signal processing which is becoming an emerging topic among an interdisciplinary community of researchers. This book is aimed at postgraduate and beginning level research scholars who would like to work in the field of Fractional Order Signal processing (FOSP). The readers should have preliminary knowledge about basic signal processing techniques. Prerequisite knowledge of fractional calculus is not essential and is exposited at relevant places in connection to the appropriate signal processing topics. Basic signal processing techniques like filtering, estimation, system identification, etc. in the light of fractional order calculus are presented along with relevant application areas. The readers can easily extend these concepts to varied disciplines like image or speech processing, pattern recognition, time series forecasting, financial data analysis and modeling, traffic modeling in communication channels, optics, biomedical signal processing, electrochemical applications and many more. Adequate references are provided in each category so that the researchers can delve deeper into each area and broaden their horizon of understanding. Available MATLAB tools to simulate FOSP theories are also introduced so that the readers can apply the theoretical concepts right-away and gain practical insight in the specific domain.
Progress In Systems Engineering
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Author : Henry Selvaraj
language : en
Publisher: Springer
Release Date : 2014-08-12
Progress In Systems Engineering written by Henry Selvaraj and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-12 with Technology & Engineering categories.
This collection of proceedings from the International Conference on Systems Engineering, Las Vegas, 2014 is orientated toward systems engineering, including topics like aero-space, power systems, industrial automation and robotics, systems theory, control theory, artificial intelligence, signal processing, decision support, pattern recognition and machine learning, information and communication technologies, image processing, and computer vision as well as its applications. The volume’s main focus is on models, algorithms, and software tools that facilitate efficient and convenient utilization of modern achievements in systems engineering.
Advances In The Theory And Applications Of Non Integer Order Systems
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Author : Wojciech Mitkowski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-03
Advances In The Theory And Applications Of Non Integer Order Systems written by Wojciech Mitkowski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-03 with Technology & Engineering categories.
This volume presents various aspects of non-integer order systems, also known as fractional systems, which have recently attracted an increasing attention in the scientific community of systems science, applied mathematics, control theory. Non-integer systems have become relevant for many fields of science and technology exemplified by the modeling of signal transmission, electric noise, dielectric polarization, heat transfer, electrochemical reactions, thermal processes, acoustics, etc. The content is divided into six parts, every of which considers one of the currently relevant problems. In the first part the Realization problem is discussed, with a special focus on positive systems. The second part considers stability of certain classes of non-integer order systems with and without delays. The third part is focused on such important aspects as controllability, observability and optimization especially in discrete time. The fourth part is focused on distributed systems where non-integer calculus leads to new and interesting results. The next part considers problems of solutions and approximations of non-integer order equations and systems. The final and most extensive part is devoted to applications. Problems from mechatronics, biomedical engineering, robotics and others are all analyzed and solved with tools from fractional systems. This volume came to fruition thanks to high level of talks and interesting discussions at RRNR 2013 - 5th Conference on Non-integer Order Calculus and its Applications that took place at AGH University of Science and Technology in Kraków, Poland, which was organized by the Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering.