实例介绍
【实例简介】
关于分数阶系统的详细介绍，包括分数阶系统的建模、分析、控制、仿真等方面的内容。
NONLINEAR PHYSICAL SCIENCE Nonlinear physical Science focuses on recent advances of fundamental theories and principles, analytical and symbolic approaches, as well as computational techniques in nonlinear physical science and nonlinear mathematics with engineering applica Topics of interest in Nonlinear Physical science include but are not limited to New findings and discoveries in nonlinear physics and mathematics Nonlinearity, complexity and mathematical structures in nonlinear physics Nonlinear phenomena and observations in nature and engineering Computational methods and theories in complex systems Lie group analysis, new theories and principles in mathematical modeling Stability, bifurcation, chaos and fractals in physical science and engineering Nonlinear chemical and biological physics Discontinuity, synchronization and natural complexity in the physical sciences SERIES EDITORS Albert C.. Luo Nail H. ibragimov Department of Mechanical and Industrial Department of Mathematics and Science Er Blekinge Institute of Technology Southern Illinois University Edwardsville S-371 79 Karlskrona. Sweden Edwardsville. IL 62026-1805 USA Email: nib abthse Email: aluo@siue. edu INTERNATIONAL ADVISORY BOARD Ping Ao, University of Washington, USA; Email: aoping@ u. washington. edu Jan Awrejcewicz, The Technical University of Lodz, Poland; Email: awrejcew@ p lodz. pl Eugene Benilov, University of Limerick, Ireland; Email: Eugene Benilov @ul.ie Eshel Ben-Jacob, Tel Aviv University, Israel; Email: eshel@tamar. tau. ac il Maurice Courbage, Universite Paris 7, France; Email: maurice courbage@ univ-paris-diderot fr Marian Gidea, Northeastern Illinois University, USA; Email: mgidea neiu edu James A Glazier, Indiana University, USA; Email: glazier @indiana. edu ShijunLiao,ShanghaiJiaotongUniversity,China;Email:sjliao@sjtu.edu.cn Jose Antonio Tenreiro Machado, ISEP-Institute of Engineering of Porto, Portugal; Email: jtm@dee isep. ipp. pt Nikolai A. Magnitskii, Russian Academy of Sciences, Russia; Email: nmag@isa.ru Josep J. Masdemont, Universitat Politecnica de Catalunya(UPC), Spain; Email: josep@ barquins. upc. edu Dmitry e Pelinovsky, McMaster University, Canada; Email: dmpeli @ math.mcmaster.ca Sergey prants, V.I. Il'ichev Pacific Oceanological Institute of the russian Academy of Sciences, Russia; pr ts@poi dvo. ru Victor I Shrira, Keele University, UK; Email: v.i. shrira@ keele.acu Jian Qiao Sun, University of California, USA; Email: jqsun@ ucmerced edu Abdul-Majid Wazwaz, Saint Xavier University, USA; Email: wazwaz@sxu. edu Pei Yu, The University of Western Ontario, Canada; Email: pyu@uwo.ca Ivo Petras Fractional-Order Nonlinear Systems Modeling, Analysis and simulation With 119 figures 高"敖育出服社 S HIGHER EDUCATION PRESS pringer Author Ivo Petras Technical University of Kosice, Faculty of BERG Institute of Control and Information of Production Processes, B. Nemcovej 3 042 00 Kosice, Slovak republic Email: ivo petras@@ tuke. sk ISSN1867-8440 e-ISSN1867-8459 Nonlinear physical science ISBN978-7-04-031534-9 Higher Education Press, Beijin ISBN978-3-642-18100-9 e-ISBN978-3-642-18101-6 Springer Heidelberg Dordrecht London New York Library of congress control number: 2011920976 C Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the german Copyright Law of September 9 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Printed on acid-free paper SpringerispartofSpringerScience+businessMedia(www.springer.com) This book is dedicated to my entire family, my parents Stefan and Erika, and my sister Petra for their understanding and support Preface The aim of the book is to present a survey of a new class of chaotic systems, the so called fractional-order chaotic systems. This book can also be used as a textbook for courses related to nonlinear systems, fractional-order systems, etc. The book is suitable for advanced undergraduate and graduate students. It is a sort of a guide to fractional-order chaotic systems that features material from original research papers including the authors own studies. The book is organized as follows: Chapter l is a brief introduction to fractional-order chaotic systems Chapter 2 provides fundamentals of fractional calculus, its properties and integral transfer methods. Three well-known definitions of fractional derivatives/integrals and methods for their numerical approximation are presented Chapter 3 includes a presentation of fractional-order systems, their descrip tion and properties. Fractional linear time-invariant (LTD, nonlinear systems, and fractional-order controllers are considered tems. The stability of interval fractional-order system is also investigated ear)sys- Chapter 4 is devoted to stability of the fra 1-order (lti and nonlin Chapter 5 contains a survey of various fractional-order chaotic systems with the total order less than three. The well-known systems such as, for example, Chuas oscillator, Lorenz's system, Rossler's system, Duffings system, and some other sys tems, for instance, Voltas system, are analyzed as well Chapter 6 begins with the introduction to control strategies of the fractional-order chaotic systems. Three general approaches: feed-back control, Sliding mode control and synchronization are described Other strategies are mentioned and discussed as well Chapter 7 concludes this book by some additional remarks Appendix a lists Matlab functions used for simulation of the fractional-order chaotic systems described in Chapter 5 fino ppendix b lists a laplace transform and inverse Laplace transform table of the A ctions used in fractional calculus Kosice, April, 2010 Ivo Petras Acknowledgements Besides new results, this book also presents results which have been already pub- lished by the author in several journal papers and conference articles during last almost 10 years. Because a portion of the material from these publications is reused n this book, the copyright permission was granted from several publishers Acknowledgement is given to Springer Science+Business Media for kind per- mission to reproduce a portion of the material from the following papers Petras I, Chaos in the fractional-order Voltas system: modeling and simulation, Nonlinear Dynamics, vol. 57, no 1-2, 2009, pp. 157-170, DOI: 10.1007/s11071 008-9429-0. Acknow ledgement is given to the Institute of Electrical and Electronic Engineers (EEE) for permission to reprint portions of the material from the following papers C [2009] IEEE Petras I, Chen Y.Q. and Coopmans C, Fractional-order mem ristive systems, Proc. of the IEEE Conference on Emerging Technologies fac tory Automation, ETFA 2009, 22-25 Sept, 2009, Palma de mallorca, Spain, DOI 10.1109/ETFA.2009.5347142 C[2009] IEEE. Petras I and Bednarova D, Fractional-order chaotic systems Proc. Of the IEEE Conference on Emerging Technologies Factory Automation, ETFA 2009, 22-25 Sept, 2009, Palma de mallorca, Spain, DOⅠ:10.1109ETFA.2009.5347112 C[2009] IEEE. Chen Y.Q., Petras I and Xue D, Fractional order control A tutorial, Proc. of the American Control Conference, ACC 2009., 10-12 June, 2009,st. Louis,USA,pp.1397-14l1,DOl:10.1109ACC.2009.5160719. C [2006] IEEE Petras I, A Note on the Fractional-Order Cellular Neural Net- works, Proc. of the International Joint Conference on Neural Networks, 16-21 July, 2006, Vancouver, Canada, pp. 1021-1024, DOI: 10.1109/JCNN2006246798 .C[2004] IEEE. Petras I, Chen Y.Q., Vinagre B M. and Podlubny, I, Stability of linear time invariant systems with interval fractional orders and interval coet ficients, Proc. of the Second IEEE International Conference on Computational Cybernetics, ICCC 2004, Aug 30-Sep 1, 2004, Vienna, Austria, pp 341-346, DOI:10.1109/ CCCYE.2004.1437745 【实例截图】
【核心代码】
关于分数阶系统的详细介绍，包括分数阶系统的建模、分析、控制、仿真等方面的内容。
NONLINEAR PHYSICAL SCIENCE Nonlinear physical Science focuses on recent advances of fundamental theories and principles, analytical and symbolic approaches, as well as computational techniques in nonlinear physical science and nonlinear mathematics with engineering applica Topics of interest in Nonlinear Physical science include but are not limited to New findings and discoveries in nonlinear physics and mathematics Nonlinearity, complexity and mathematical structures in nonlinear physics Nonlinear phenomena and observations in nature and engineering Computational methods and theories in complex systems Lie group analysis, new theories and principles in mathematical modeling Stability, bifurcation, chaos and fractals in physical science and engineering Nonlinear chemical and biological physics Discontinuity, synchronization and natural complexity in the physical sciences SERIES EDITORS Albert C.. Luo Nail H. ibragimov Department of Mechanical and Industrial Department of Mathematics and Science Er Blekinge Institute of Technology Southern Illinois University Edwardsville S-371 79 Karlskrona. Sweden Edwardsville. IL 62026-1805 USA Email: nib abthse Email: aluo@siue. edu INTERNATIONAL ADVISORY BOARD Ping Ao, University of Washington, USA; Email: aoping@ u. washington. edu Jan Awrejcewicz, The Technical University of Lodz, Poland; Email: awrejcew@ p lodz. pl Eugene Benilov, University of Limerick, Ireland; Email: Eugene Benilov @ul.ie Eshel Ben-Jacob, Tel Aviv University, Israel; Email: eshel@tamar. tau. ac il Maurice Courbage, Universite Paris 7, France; Email: maurice courbage@ univ-paris-diderot fr Marian Gidea, Northeastern Illinois University, USA; Email: mgidea neiu edu James A Glazier, Indiana University, USA; Email: glazier @indiana. edu ShijunLiao,ShanghaiJiaotongUniversity,China;Email:sjliao@sjtu.edu.cn Jose Antonio Tenreiro Machado, ISEP-Institute of Engineering of Porto, Portugal; Email: jtm@dee isep. ipp. pt Nikolai A. Magnitskii, Russian Academy of Sciences, Russia; Email: nmag@isa.ru Josep J. Masdemont, Universitat Politecnica de Catalunya(UPC), Spain; Email: josep@ barquins. upc. edu Dmitry e Pelinovsky, McMaster University, Canada; Email: dmpeli @ math.mcmaster.ca Sergey prants, V.I. Il'ichev Pacific Oceanological Institute of the russian Academy of Sciences, Russia; pr ts@poi dvo. ru Victor I Shrira, Keele University, UK; Email: v.i. shrira@ keele.acu Jian Qiao Sun, University of California, USA; Email: jqsun@ ucmerced edu Abdul-Majid Wazwaz, Saint Xavier University, USA; Email: wazwaz@sxu. edu Pei Yu, The University of Western Ontario, Canada; Email: pyu@uwo.ca Ivo Petras Fractional-Order Nonlinear Systems Modeling, Analysis and simulation With 119 figures 高"敖育出服社 S HIGHER EDUCATION PRESS pringer Author Ivo Petras Technical University of Kosice, Faculty of BERG Institute of Control and Information of Production Processes, B. Nemcovej 3 042 00 Kosice, Slovak republic Email: ivo petras@@ tuke. sk ISSN1867-8440 e-ISSN1867-8459 Nonlinear physical science ISBN978-7-04-031534-9 Higher Education Press, Beijin ISBN978-3-642-18100-9 e-ISBN978-3-642-18101-6 Springer Heidelberg Dordrecht London New York Library of congress control number: 2011920976 C Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the german Copyright Law of September 9 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Printed on acid-free paper SpringerispartofSpringerScience+businessMedia(www.springer.com) This book is dedicated to my entire family, my parents Stefan and Erika, and my sister Petra for their understanding and support Preface The aim of the book is to present a survey of a new class of chaotic systems, the so called fractional-order chaotic systems. This book can also be used as a textbook for courses related to nonlinear systems, fractional-order systems, etc. The book is suitable for advanced undergraduate and graduate students. It is a sort of a guide to fractional-order chaotic systems that features material from original research papers including the authors own studies. The book is organized as follows: Chapter l is a brief introduction to fractional-order chaotic systems Chapter 2 provides fundamentals of fractional calculus, its properties and integral transfer methods. Three well-known definitions of fractional derivatives/integrals and methods for their numerical approximation are presented Chapter 3 includes a presentation of fractional-order systems, their descrip tion and properties. Fractional linear time-invariant (LTD, nonlinear systems, and fractional-order controllers are considered tems. The stability of interval fractional-order system is also investigated ear)sys- Chapter 4 is devoted to stability of the fra 1-order (lti and nonlin Chapter 5 contains a survey of various fractional-order chaotic systems with the total order less than three. The well-known systems such as, for example, Chuas oscillator, Lorenz's system, Rossler's system, Duffings system, and some other sys tems, for instance, Voltas system, are analyzed as well Chapter 6 begins with the introduction to control strategies of the fractional-order chaotic systems. Three general approaches: feed-back control, Sliding mode control and synchronization are described Other strategies are mentioned and discussed as well Chapter 7 concludes this book by some additional remarks Appendix a lists Matlab functions used for simulation of the fractional-order chaotic systems described in Chapter 5 fino ppendix b lists a laplace transform and inverse Laplace transform table of the A ctions used in fractional calculus Kosice, April, 2010 Ivo Petras Acknowledgements Besides new results, this book also presents results which have been already pub- lished by the author in several journal papers and conference articles during last almost 10 years. Because a portion of the material from these publications is reused n this book, the copyright permission was granted from several publishers Acknowledgement is given to Springer Science+Business Media for kind per- mission to reproduce a portion of the material from the following papers Petras I, Chaos in the fractional-order Voltas system: modeling and simulation, Nonlinear Dynamics, vol. 57, no 1-2, 2009, pp. 157-170, DOI: 10.1007/s11071 008-9429-0. Acknow ledgement is given to the Institute of Electrical and Electronic Engineers (EEE) for permission to reprint portions of the material from the following papers C [2009] IEEE Petras I, Chen Y.Q. and Coopmans C, Fractional-order mem ristive systems, Proc. of the IEEE Conference on Emerging Technologies fac tory Automation, ETFA 2009, 22-25 Sept, 2009, Palma de mallorca, Spain, DOI 10.1109/ETFA.2009.5347142 C[2009] IEEE. Petras I and Bednarova D, Fractional-order chaotic systems Proc. Of the IEEE Conference on Emerging Technologies Factory Automation, ETFA 2009, 22-25 Sept, 2009, Palma de mallorca, Spain, DOⅠ:10.1109ETFA.2009.5347112 C[2009] IEEE. Chen Y.Q., Petras I and Xue D, Fractional order control A tutorial, Proc. of the American Control Conference, ACC 2009., 10-12 June, 2009,st. Louis,USA,pp.1397-14l1,DOl:10.1109ACC.2009.5160719. C [2006] IEEE Petras I, A Note on the Fractional-Order Cellular Neural Net- works, Proc. of the International Joint Conference on Neural Networks, 16-21 July, 2006, Vancouver, Canada, pp. 1021-1024, DOI: 10.1109/JCNN2006246798 .C[2004] IEEE. Petras I, Chen Y.Q., Vinagre B M. and Podlubny, I, Stability of linear time invariant systems with interval fractional orders and interval coet ficients, Proc. of the Second IEEE International Conference on Computational Cybernetics, ICCC 2004, Aug 30-Sep 1, 2004, Vienna, Austria, pp 341-346, DOI:10.1109/ CCCYE.2004.1437745 【实例截图】
【核心代码】
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