| Description |
1 online resource |
| Contents |
Intro; Preface; Acknowledgements; Contents; Abbreviations; List of Figures; 1 Introduction; 1.1 Cyber-Physical Systems and Distributed Parameter Systems; 1.1.1 Cyber-Physical Systems; 1.1.2 Distributed Parameter Systems; 1.2 New Challenges; 1.3 Continuous Time Random Walk and Fractional Dynamics Approach; 1.3.1 Continuous Time Random Walk; 1.3.2 Fractional Dynamics Approach; 1.4 Regional Analysis via Actuators and Sensors; 1.4.1 Actuators; 1.4.2 Sensors; 1.4.3 Regional Analysis and the Emerging Research Opportunities; References; 2 Preliminary Results |
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2.1 Special Functions and Their Properties2.1.1 The Gamma Function and Its Related Special Functions; 2.1.2 The Mittag-Leffler Functions and Their Properties; 2.2 Fractional Calculus; 2.2.1 Backgrounds; 2.2.2 Riemann -- Liouville Fractional Integrals; 2.2.3 Riemann -- Liouville Fractional Derivatives; 2.2.4 Caputo Fractional Derivatives; 2.3 C0-Semigroups; 2.4 Hilbert Uniqueness Methods; References; 3 Regional Controllability; 3.1 Regional Controllability; 3.1.1 Riemann -- Liouville-Type Time Fractional Diffusion Systems; 3.1.2 Caputo-Type Time Fractional Diffusion Systems |
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3.2 Regional Gradient Controllability3.2.1 Riemann -- Liouville-Type Time Fractional Diffusion Systems; 3.2.2 Caputo-Type Time Fractional Diffusion Systems; 3.3 Regional Boundary Controllability; 3.3.1 Riemann -- Liouville-Type Time Fractional Diffusion Systems; 3.3.2 Caputo-Type Time Fractional Diffusion Systems; 3.4 Notes and Remarks; References; 4 Regional Observability; 4.1 Regional Observability; 4.1.1 Riemann -- Liouville-Type Time Fractional Diffusion Systems; 4.1.2 Caputo-Type Time Fractional Diffusion Systems; 4.2 Regional Gradient Observability |
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4.2.1 Riemann -- Liouville-Type Time Fractional Diffusion Systems4.2.2 Caputo-Type Time Fractional Diffusion Systems; 4.3 Regional Boundary Observability; 4.3.1 Riemann -- Liouville-Type Time Fractional Diffusion Systems; 4.3.2 Caputo-Type Time Fractional Diffusion Systems; 4.4 Notes and Remarks; References; 5 Regional Detection of Unknown Sources; 5.1 Preliminary Results; 5.1.1 Sources; 5.1.2 Detection; 5.2 Riemannâ#x80;#x93;Liouville-Type Time Fractional Diffusion Systems; 5.2.1 Problem Statement; 5.2.2 Regional Strategic Sensors and Regional Spy Sensors |
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5.2.3 Reconstruction of a Regionally Detectable Source5.2.4 Several Examples; 5.3 Caputo-Type Time Fractional Diffusion Systems; 5.3.1 Problem Formulation; 5.3.2 The Relationships Between Strategic Sensors and Spy Sensors in Ï#x89;; 5.3.3 An Approach to Regionally Detect the Source; 5.3.4 An Example; 5.4 Notes and Remarks; References; 6 Spreadability; 6.1 The Basic Knowledge of Spreadability; 6.2 Riemann -- Liouville-Type Time Fractional Diffusion Systems; 6.2.1 Spreading Control Problem; 6.2.2 Adaptive Spreading Control Problems; 6.3 Caputo-Type Time Fractional Diffusion Systems |
| Summary |
This monograph provides an accessible introduction to the regional analysis of fractional diffusion processes. It begins with background coverage of fractional calculus, functional analysis, distributed parameter systems and relevant basic control theory. New research problems are then defined in terms of their actuation and sensing policies within the regional analysis framework. The results presented provide insight into the control-theoretic analysis of fractional-order systems for use in real-life applications such as hard-disk drives, sleep stage identification and classification, and unmanned aerial vehicle control. The results can also be extended to complex fractional-order distributed-parameter systems and various open questions with potential for further investigation are discussed. For instance, the problem of fractional order distributed-parameter systems with mobile actuators/sensors, optimal parameter identification, optimal locations/trajectory of actuators/sensors and regional actuation/sensing configurations are of great interest. The book?s use of illustrations and consistent examples throughout helps readers to understand the significance of the proposed fractional models and methodologies and to enhance their comprehension. The applications treated in the book run the gamut from environmental science to national security. Academics and graduate students working with cyber-physical and distributed systems or interested in the the applications of fractional calculus will find this book to be an instructive source of state-of-the-art results and inspiration for further research |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Vendor-supplied metadata |
| Subject |
Diffusion processes.
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Cooperating objects (Computer systems)
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Distributed parameter systems.
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Functional analysis & transforms.
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Cybernetics & systems theory.
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Automatic control engineering.
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MATHEMATICS -- Applied.
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MATHEMATICS -- Probability & Statistics -- General.
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Cooperating objects (Computer systems)
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Diffusion processes
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Distributed parameter systems
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| Form |
Electronic book
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| Author |
Chen, YangQuan, 1966- author.
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Kou, Chunhai, author
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| ISBN |
9783319728964 |
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3319728962 |
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