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BL
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| Record Number
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860708
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| Main Entry
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Anfinsen, Henrik
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| Title & Author
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Adaptive control of hyperbolic PDEs /\ Henrik Anfinsen, Ole Morten Aamo.
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| Publication Statement
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Cham, Switzerland :: Springer,, [2019]
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| Series Statement
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Communications and control engineering
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| Page. NO
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1 online resource
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| ISBN
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3030058794
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: 9783030058791
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3030058786
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9783030058784
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| Notes
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9.3.3 Control Law
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| Contents
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Intro; Preface; Acknowledgements; Contents; Part I Background; 1 Background; 1.1 Introduction; 1.2 Notation; 1.3 Linear Hyperbolic PDEs; 1.4 Classes of Linear Hyperbolic PDEs Considered; 1.4.1 Scalar Systems; 1.4.2 2times2 Systems; 1.4.3 n + 1 Systems; 1.4.4 n + m Systems; 1.5 Collocated Versus Anti-collocated Sensing and Control; 1.6 Stability of PDEs; 1.7 Some Useful Properties of Linear Hyperbolic PDEs; 1.8 Volterra Integral Transformations; 1.8.1 Time-Invariant Volterra Integral Transformations; 1.8.2 Time-Variant Volterra Integral Transformations
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1.8.3 Affine Volterra Integral Transformations1.9 The Infinite-Dimensional Backstepping Technique for PDEs; 1.10 Approaches to Adaptive Control of PDEs; 1.10.1 Lyapunov Design; 1.10.2 Identifier-Based Design; 1.10.3 Swapping-Based Design; 1.10.4 Discussion of the Three Methods; References; Part II Scalar Systems; 2 Introduction; 2.1 System Equations; 2.2 Proof of Lemma2.1; References; 3 Non-adaptive Schemes; 3.1 Introduction; 3.2 State Feedback Controller; 3.2.1 Controller Design; 3.2.2 Explicit Controller Gains; 3.3 Boundary Observer; 3.4 Output Feedback Controller
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3.5 Output Tracking Controller3.6 Simulations; 3.7 Notes; Reference; 4 Adaptive State-Feedback Controller; 4.1 Introduction; 4.2 Identifier-Based Design; 4.2.1 Identifier and Update Law; 4.2.2 Control Law; 4.2.3 Backstepping and Target System; 4.2.4 Proof of Theorem4.1; 4.3 Simulations; 4.4 Notes; Reference; 5 Adaptive Output-Feedback Controller; 5.1 Introduction; 5.2 Swapping-Based Design; 5.2.1 Filter Design and Non-adaptive State Estimates; 5.2.2 Adaptive Laws and State Estimation; 5.2.3 Control Law; 5.2.4 Backstepping and Target System; 5.2.5 Proof of Theorem5.1; 5.3 Simulations
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5.4 NotesReferences; 6 Model Reference Adaptive Control; 6.1 Introduction; 6.2 Model Reference Adaptive Control; 6.2.1 Canonical Form; 6.2.2 Filter Design and Non-adaptive State Estimate; 6.2.3 Adaptive Laws and State Estimates; 6.2.4 Control Law; 6.2.5 Backstepping; 6.2.6 Proof of Theorem 6.1; 6.3 Adaptive Output Feedback Stabilization; 6.4 Simulation; 6.5 Notes; References; Part III 2 times2 Systems; 7 Introduction; References; 8 Non-adaptive Schemes; 8.1 Introduction; 8.2 State Feedback Controller; 8.3 State Observers; 8.3.1 Sensing Anti-collocated with Actuation
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8.3.2 Sensing Collocated with Actuation8.4 Output Feedback Controllers; 8.4.1 Sensing Anti-collocated with Actuation; 8.4.2 Sensing Collocated with Actuation; 8.5 Output Tracking Controller; 8.6 Simulations; 8.7 Notes; References; 9 Adaptive State Feedback Controllers; 9.1 Introduction; 9.2 Identifier-Based Design for a System with Constant Coefficients; 9.2.1 Identifier and Adaptive Laws; 9.2.2 Control Law; 9.2.3 Backstepping Transformation; 9.2.4 Proof of Theorem 9.1; 9.3 Swapping-Based Design for a System with Spatially Varying Coefficients; 9.3.1 Filter Design; 9.3.2 Adaptive Laws
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| Abstract
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Adaptive Control of Linear Hyperbolic PDEs provides a comprehensive treatment of adaptive control of linear hyperbolic systems, using the backstepping method. It develops adaptive control strategies for different combinations of measurements and actuators, as well as for a range of different combinations of parameter uncertainty. The book treats boundary control of systems of hyperbolic partial differential equations (PDEs) with uncertain parameters. The authors develop designs for single equations, as well as any number of coupled equations. The designs are accompanied by mathematical proofs, which allow the reader to gain insight into the technical challenges associated with adaptive control of hyperbolic PDEs, and to get an overview of problems that are still open for further research. Although stabilization of unstable systems by boundary control and boundary sensing are the particular focus, state-feedback designs are also presented. The book also includes simulation examples with implementational details and graphical displays, to give readers an insight into the performance of the proposed control algorithms, as well as the computational details involved. A library of MATLAB® code supplies ready-to-use implementations of the control and estimation algorithms developed in the book, allowing readers to tailor controllers for cases of their particular interest with little effort. These implementations can be used for many different applications, including pipe flows, traffic flow, electrical power lines, and more. Adaptive Control of Linear Hyperbolic PDEs is of value to researchers and practitioners in applied mathematics, engineering and physics; it contains a rich set of adaptive control designs, including mathematical proofs and simulation demonstrations. The book is also of interest to students looking to expand their knowledge of hyperbolic PDEs.
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| Subject
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Adaptive control systems.
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| Subject
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Differential equations, Hyperbolic.
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Differential equations, Partial.
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| Subject
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Adaptive control systems.
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| Subject
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Differential equations, Hyperbolic.
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| Subject
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Differential equations, Partial.
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| Subject
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TECHNOLOGY ENGINEERING-- Engineering (General)
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| Dewey Classification
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629.8/36
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| LC Classification
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TJ217.A54 2019
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| Added Entry
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Aamo, Ole Morten
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