The Resource Adaptive control of parabolic PDEs, Andrey Smyshlyaev and Miroslav Krstic

Adaptive control of parabolic PDEs, Andrey Smyshlyaev and Miroslav Krstic

Label
Adaptive control of parabolic PDEs
Title
Adaptive control of parabolic PDEs
Statement of responsibility
Andrey Smyshlyaev and Miroslav Krstic
Creator
Contributor
Subject
Genre
Language
  • eng
  • eng
Summary
This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems. Andrey Smyshlyaev and Miroslav Krstic develop explicit feedback laws that do not require real-time solution of Riccati or other algebraic operator-valued equations. The book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree. The book al
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Smyshlyaev, Andrey
Dewey number
  • 515.3534
  • 515/.3534
Index
index present
Language note
English
LC call number
QA374
LC item number
.S59 2010
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Krstić, Miroslav
http://library.link/vocab/subjectName
  • Differential equations, Parabolic
  • Distributed parameter systems
  • Adaptive control systems
Label
Adaptive control of parabolic PDEs, Andrey Smyshlyaev and Miroslav Krstic
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Contents
  • 1.4.
  • 6.6.
  • Observer Design for the Ginzburg-Landau Equation
  • 6.7.
  • Output Feedback for the Ginzburg-Landau Equation
  • 6.8.
  • Simulations with the Nonlinear Ginzburg-Landau Equation
  • 6.9.
  • Notes and References
  • PART II.
  • ADAPTIVE SCHEMES
  • Backstepping
  • Chapter 7.
  • Systematization of Approaches to Adaptive Boundary Stabilization of PDEs
  • 7.1.
  • Categorization of Adaptive Controllers and Identifiers
  • 7.2.
  • Benchmark Systems
  • 7.3.
  • Controllers
  • 7.4.
  • Lyapunov Design
  • 1.5.
  • 7.5.
  • Certainty Equivalence Designs
  • 7.6.
  • Trade-offs between the Designs
  • 7.7.
  • Stability
  • 7.8.
  • Notes and References
  • Chapter 8.
  • Lyapunov-Based Designs
  • Explicitly Parametrized Controllers
  • 8.1.
  • Plant with Unknown Reaction Coefficient
  • 8.2.
  • Proof of Theorem 8.1
  • 8.3.
  • Well-Posedness of the Closed-Loop System
  • 8.4.
  • Parametric Robustness
  • 8.5.
  • Alternative Approach
  • 1.6.
  • 8.6.
  • Other Benchmark Problems
  • 8.7.
  • Systems with Unknown Diffusion and Advection Coefficients
  • 8.8.
  • Simulation Results
  • 8.9.
  • Notes and References
  • Chapter 9.
  • Certainty Equivalence Design with Passive Identifiers
  • Adaptive Control
  • 9.1.
  • Benchmark Plant
  • 9.2.
  • 3D Reaction-Advection-Diffusion Plant
  • 9.3.
  • Proof of Theorem 9.2
  • 9.4.
  • Simulations
  • 9.5.
  • Notes and References
  • 1.7.
  • Chapter 10.
  • Certainty Equivalence Design with Swapping Identifiers
  • 10.1.
  • Reaction-Advection-Diffusion Plant
  • 10.2.
  • Proof of Theorem 10.1
  • 10.3.
  • Simulations
  • 10.4.
  • Notes and References
  • Overview of the Literature on Adaptive Control for Parabolic PDEs
  • Chapter 11.
  • State Feedback for PDEs with Spatially Varying Coefficients
  • 11.1.
  • Problem Statement
  • 11.2.
  • Nominal Control Design
  • 11.3.
  • Robustness to Error in Gain Kernel
  • 11.4.
  • Lyapunov Design
  • 1.8.
  • 11.5.
  • Lyapunov Design for Plants with Unknown Advection and Diffusion Parameters
  • 11.6.
  • Passivity-Based Design
  • 11.7.
  • Simulations
  • 11.8.
  • Notes and References
  • Chapter 12.
  • Closed-Form Adaptive Output-Feedback Contollers
  • Inverse Optimality
  • 12.1.
  • Lyapunov Design---Plant with Unknown Parameter in the Domain
  • 12.2.
  • Lyapunov Design---Plant with Unknown Parameter in the Boundary Condition
  • 12.3.
  • Swapping Design---Plant with Unknown Parameter in the Domain
  • 12.4.
  • Swapping Design---Plant with Unknown Parameter in the Boundary Condition
  • 12.5.
  • Simulations
  • Chapter 1.
  • 1.9.
  • 12.6.
  • Notes and References
  • Chapter 13.
  • Output Feedback for PDEs with Spatially Varying Coefficients
  • 13.1.
  • Reaction-Advection-Diffusion Plant
  • 13.2.
  • Transformation to Observer Canonical Form
  • 13.3.
  • Nominal Controller
  • Organization of the Book
  • 13.4.
  • Filters
  • 13.5.
  • Frequency Domain Compensator with Frozen Parameters
  • 13.6.
  • Update Laws
  • 13.7.
  • Stability
  • 13.8.
  • Trajectory Tracking
  • 1.10.
  • 13.9.
  • Ginzburg-Landau Equation
  • 13.10.
  • Identifier for the Ginzburg-Landau Equation
  • 13.11.
  • Stability of Adaptive Scheme for the Ginzburg-Landau Equation
  • 13.12.
  • Simulations
  • 13.13.
  • Notes and References
  • Notation
  • Chapter 14.
  • Inverse Optimal Control
  • 14.1.
  • Nonadaptive Inverse Optimal Control
  • 14.2.
  • Reducing Control Effort through Adaptation
  • 14.3.
  • Dirichlet Actuation
  • 14.4.
  • Design Example
  • PART I.
  • 14.5.
  • Comparison with the LQR Approach
  • 14.6.
  • Inverse Optimal Adaptive Control
  • 14.7.
  • Stability and Inverse Optimality of the Adaptive Scheme
  • 14.8.
  • Notes and References
  • Appendix A.
  • Adaptive Backstepping for Nonlinear ODEs---The Basics
  • NONADAPTIVE CONTROLLERS
  • A.1.
  • Nonadaptive Backstepping---The Known Parameter Case
  • A.2.
  • Tuning Functions Design
  • A.3.
  • Modular Design
  • A.4.
  • Output Feedback Designs
  • A.5.
  • Extensions
  • Chapter 2.
  • Appendix B.
  • Poincare and Agmon Inequalities
  • Appendix C.
  • Bessel Functions
  • C.1.
  • Bessel Function Jn
  • C.2.
  • Modified Bessel Function In
  • Appendix D.
  • Barbalat's and Other Lemmas for Proving Adaptive Regulation
  • State Feedback
  • Appendix E.
  • Basic Parabolic PDEs and Their Exact Solutions
  • E.1.
  • Reaction-Diffusion Equation with Dirichlet Boundary Conditions
  • E.2.
  • Reaction-Diffusion Equation with Neumann Boundary Conditions
  • E.3.
  • Reaction-Diffusion Equation with Mixed Boundary Conditions
  • 2.1.
  • Problem Formulation
  • Introduction
  • 2.2.
  • Backstepping Transformation and PDE for Its Kernel
  • 2.3.
  • Converting the PDE into an Integral Equation
  • 2.4.
  • Analysis of the Integral Equation by Successive Approximation Series
  • 2.5.
  • Stability of the Closed-Loop System
  • 2.6.
  • Dirichlet Uncontrolled End
  • 1.1.
  • 2.7.
  • Neumann Actuation
  • 2.8.
  • Simulation
  • 2.9.
  • Discussion
  • 2.10.
  • Notes and References
  • Chapter 3.
  • Closed-Form Controllers
  • Parabolic and Hyperbolic PDE Systems
  • 3.1.
  • Reaction-Diffusion Equation
  • 3.2.
  • Family of Plants with Spatially Varying Reactivity
  • 3.3.
  • Solid Propellant Rocket Model
  • 3.4.
  • Plants with Spatially Varying Diffusivity
  • 3.5.
  • Time-Varying Reaction Equation
  • 1.2.
  • 3.6.
  • More Complex Systems
  • 3.7.
  • 2D and 3D Systems
  • 3.8.
  • Notes and References
  • Chapter 4.
  • Observers
  • 4.1.
  • Observer Design for the Anti-Collocated Setup
  • Roles of PDE Plant Instability, Actuator Location, Uncertainty Structure, Relative Degree, and Functional Parameters
  • 4.2.
  • Plants with Dirichlet Uncontrolled End and Neumann Measurements
  • 4.3.
  • Observer Design for the Collocated Setup
  • 4.4.
  • Notes and References
  • Chapter 5.
  • Output Feedback
  • 5.1.
  • Anti-Collocated Setup
  • 1.3.
  • 5.2.
  • Collocated Setup
  • 5.3.
  • Closed-Form Compensators
  • 5.4.
  • Frequency Domain Compensator
  • 5.5.
  • Notes and References
  • Chapter 6.
  • Control of Complex-Valued PDEs
  • Class of Parabolic PDE Systems
  • 6.1.
  • State-Feedback Design for the Schrodinger Equation
  • 6.2.
  • Observer Design for the Schrodinger Equation
  • 6.3.
  • Output-Feedback Compensator for the Schrodinger Equation
  • 6.4.
  • Ginzburg-Landau Equation
  • 6.5.
  • State Feedback for the Ginzburg-Landau Equation
Dimensions
25 cm.
Extent
xiii, 328 p.
Isbn
9780691142869
Isbn Type
(hardcover : alk. paper)
Lccn
2009048242
Other physical details
ill.
System control number
  • (CaMWU)u2130533-01umb_inst
  • 2187023
  • (Sirsi) i9780691142869
  • (OCoLC)466341418
Label
Adaptive control of parabolic PDEs, Andrey Smyshlyaev and Miroslav Krstic
Publication
Bibliography note
Includes bibliographical references and index
Contents
  • 1.4.
  • 6.6.
  • Observer Design for the Ginzburg-Landau Equation
  • 6.7.
  • Output Feedback for the Ginzburg-Landau Equation
  • 6.8.
  • Simulations with the Nonlinear Ginzburg-Landau Equation
  • 6.9.
  • Notes and References
  • PART II.
  • ADAPTIVE SCHEMES
  • Backstepping
  • Chapter 7.
  • Systematization of Approaches to Adaptive Boundary Stabilization of PDEs
  • 7.1.
  • Categorization of Adaptive Controllers and Identifiers
  • 7.2.
  • Benchmark Systems
  • 7.3.
  • Controllers
  • 7.4.
  • Lyapunov Design
  • 1.5.
  • 7.5.
  • Certainty Equivalence Designs
  • 7.6.
  • Trade-offs between the Designs
  • 7.7.
  • Stability
  • 7.8.
  • Notes and References
  • Chapter 8.
  • Lyapunov-Based Designs
  • Explicitly Parametrized Controllers
  • 8.1.
  • Plant with Unknown Reaction Coefficient
  • 8.2.
  • Proof of Theorem 8.1
  • 8.3.
  • Well-Posedness of the Closed-Loop System
  • 8.4.
  • Parametric Robustness
  • 8.5.
  • Alternative Approach
  • 1.6.
  • 8.6.
  • Other Benchmark Problems
  • 8.7.
  • Systems with Unknown Diffusion and Advection Coefficients
  • 8.8.
  • Simulation Results
  • 8.9.
  • Notes and References
  • Chapter 9.
  • Certainty Equivalence Design with Passive Identifiers
  • Adaptive Control
  • 9.1.
  • Benchmark Plant
  • 9.2.
  • 3D Reaction-Advection-Diffusion Plant
  • 9.3.
  • Proof of Theorem 9.2
  • 9.4.
  • Simulations
  • 9.5.
  • Notes and References
  • 1.7.
  • Chapter 10.
  • Certainty Equivalence Design with Swapping Identifiers
  • 10.1.
  • Reaction-Advection-Diffusion Plant
  • 10.2.
  • Proof of Theorem 10.1
  • 10.3.
  • Simulations
  • 10.4.
  • Notes and References
  • Overview of the Literature on Adaptive Control for Parabolic PDEs
  • Chapter 11.
  • State Feedback for PDEs with Spatially Varying Coefficients
  • 11.1.
  • Problem Statement
  • 11.2.
  • Nominal Control Design
  • 11.3.
  • Robustness to Error in Gain Kernel
  • 11.4.
  • Lyapunov Design
  • 1.8.
  • 11.5.
  • Lyapunov Design for Plants with Unknown Advection and Diffusion Parameters
  • 11.6.
  • Passivity-Based Design
  • 11.7.
  • Simulations
  • 11.8.
  • Notes and References
  • Chapter 12.
  • Closed-Form Adaptive Output-Feedback Contollers
  • Inverse Optimality
  • 12.1.
  • Lyapunov Design---Plant with Unknown Parameter in the Domain
  • 12.2.
  • Lyapunov Design---Plant with Unknown Parameter in the Boundary Condition
  • 12.3.
  • Swapping Design---Plant with Unknown Parameter in the Domain
  • 12.4.
  • Swapping Design---Plant with Unknown Parameter in the Boundary Condition
  • 12.5.
  • Simulations
  • Chapter 1.
  • 1.9.
  • 12.6.
  • Notes and References
  • Chapter 13.
  • Output Feedback for PDEs with Spatially Varying Coefficients
  • 13.1.
  • Reaction-Advection-Diffusion Plant
  • 13.2.
  • Transformation to Observer Canonical Form
  • 13.3.
  • Nominal Controller
  • Organization of the Book
  • 13.4.
  • Filters
  • 13.5.
  • Frequency Domain Compensator with Frozen Parameters
  • 13.6.
  • Update Laws
  • 13.7.
  • Stability
  • 13.8.
  • Trajectory Tracking
  • 1.10.
  • 13.9.
  • Ginzburg-Landau Equation
  • 13.10.
  • Identifier for the Ginzburg-Landau Equation
  • 13.11.
  • Stability of Adaptive Scheme for the Ginzburg-Landau Equation
  • 13.12.
  • Simulations
  • 13.13.
  • Notes and References
  • Notation
  • Chapter 14.
  • Inverse Optimal Control
  • 14.1.
  • Nonadaptive Inverse Optimal Control
  • 14.2.
  • Reducing Control Effort through Adaptation
  • 14.3.
  • Dirichlet Actuation
  • 14.4.
  • Design Example
  • PART I.
  • 14.5.
  • Comparison with the LQR Approach
  • 14.6.
  • Inverse Optimal Adaptive Control
  • 14.7.
  • Stability and Inverse Optimality of the Adaptive Scheme
  • 14.8.
  • Notes and References
  • Appendix A.
  • Adaptive Backstepping for Nonlinear ODEs---The Basics
  • NONADAPTIVE CONTROLLERS
  • A.1.
  • Nonadaptive Backstepping---The Known Parameter Case
  • A.2.
  • Tuning Functions Design
  • A.3.
  • Modular Design
  • A.4.
  • Output Feedback Designs
  • A.5.
  • Extensions
  • Chapter 2.
  • Appendix B.
  • Poincare and Agmon Inequalities
  • Appendix C.
  • Bessel Functions
  • C.1.
  • Bessel Function Jn
  • C.2.
  • Modified Bessel Function In
  • Appendix D.
  • Barbalat's and Other Lemmas for Proving Adaptive Regulation
  • State Feedback
  • Appendix E.
  • Basic Parabolic PDEs and Their Exact Solutions
  • E.1.
  • Reaction-Diffusion Equation with Dirichlet Boundary Conditions
  • E.2.
  • Reaction-Diffusion Equation with Neumann Boundary Conditions
  • E.3.
  • Reaction-Diffusion Equation with Mixed Boundary Conditions
  • 2.1.
  • Problem Formulation
  • Introduction
  • 2.2.
  • Backstepping Transformation and PDE for Its Kernel
  • 2.3.
  • Converting the PDE into an Integral Equation
  • 2.4.
  • Analysis of the Integral Equation by Successive Approximation Series
  • 2.5.
  • Stability of the Closed-Loop System
  • 2.6.
  • Dirichlet Uncontrolled End
  • 1.1.
  • 2.7.
  • Neumann Actuation
  • 2.8.
  • Simulation
  • 2.9.
  • Discussion
  • 2.10.
  • Notes and References
  • Chapter 3.
  • Closed-Form Controllers
  • Parabolic and Hyperbolic PDE Systems
  • 3.1.
  • Reaction-Diffusion Equation
  • 3.2.
  • Family of Plants with Spatially Varying Reactivity
  • 3.3.
  • Solid Propellant Rocket Model
  • 3.4.
  • Plants with Spatially Varying Diffusivity
  • 3.5.
  • Time-Varying Reaction Equation
  • 1.2.
  • 3.6.
  • More Complex Systems
  • 3.7.
  • 2D and 3D Systems
  • 3.8.
  • Notes and References
  • Chapter 4.
  • Observers
  • 4.1.
  • Observer Design for the Anti-Collocated Setup
  • Roles of PDE Plant Instability, Actuator Location, Uncertainty Structure, Relative Degree, and Functional Parameters
  • 4.2.
  • Plants with Dirichlet Uncontrolled End and Neumann Measurements
  • 4.3.
  • Observer Design for the Collocated Setup
  • 4.4.
  • Notes and References
  • Chapter 5.
  • Output Feedback
  • 5.1.
  • Anti-Collocated Setup
  • 1.3.
  • 5.2.
  • Collocated Setup
  • 5.3.
  • Closed-Form Compensators
  • 5.4.
  • Frequency Domain Compensator
  • 5.5.
  • Notes and References
  • Chapter 6.
  • Control of Complex-Valued PDEs
  • Class of Parabolic PDE Systems
  • 6.1.
  • State-Feedback Design for the Schrodinger Equation
  • 6.2.
  • Observer Design for the Schrodinger Equation
  • 6.3.
  • Output-Feedback Compensator for the Schrodinger Equation
  • 6.4.
  • Ginzburg-Landau Equation
  • 6.5.
  • State Feedback for the Ginzburg-Landau Equation
Dimensions
25 cm.
Extent
xiii, 328 p.
Isbn
9780691142869
Isbn Type
(hardcover : alk. paper)
Lccn
2009048242
Other physical details
ill.
System control number
  • (CaMWU)u2130533-01umb_inst
  • 2187023
  • (Sirsi) i9780691142869
  • (OCoLC)466341418

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