Adaptive control of parabolic PDEs

Adaptive control of parabolic PDEs

Zapisane w:
Opis bibliograficzny
Główni autorzy: Smyshlyaev, Andrey, Krstić, Miroslav (Autor)
Format: Livre papier
Język:Anglais
Wydane: Princeton ; Oxford : Princeton University Press cop. 2010.
Hasła przedmiotowe:
Systèmes, Théorie des
Commande, Théorie de la
Équations aux dérivées partielles
Autres localisations: Voir dans le Sudoc
Spis treści:
  • chapter 1. Introduction
  • 1.1 Parabolic and Hyperbolic PDE Systems
  • 1.2 The Roles of PDE Plant Instability, Actuator Location, Uncertainty Structure, Relative Degree, and Functional Parameters
  • 1.3 Class of Parabolic PDE Systems
  • 1.4 Backstepping
  • 1.5 Explicitly Parametrized Controllers
  • 1.6 Adaptive Control
  • 1.7 Overview of the Literature on Adaptive Control for Parabolic PDEs
  • 1.8 Inverse Optimality
  • 1.9 Organization of the Book
  • 1.10 Notation
  • part I: NONADAPTIVE CONTROLLERS
  • chapter 2. State Feedback
  • 2.1 Problem Formulation
  • 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
  • 2.7 Neumann Actuation
  • 2.8 Simulation
  • 2.9 Discussion
  • 2.10 Notes and References
  • chapter 3. Closed-Form Controllers
  • 3.1 The Reaction-Diffusion Equation
  • 3.2 A Family of Plants with Spatially Varying Reactivity
  • 3.3 Solid Propellant Rocket Model
  • 3.4 Plants with Spatially Varying Diffusivity
  • 3.5 The Time-Varying Reaction Equation
  • 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
  • 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
  • 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
  • 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 The Ginzburg-Landau Equation
  • 6.5 State Feedback for the Ginzburg-Landau Equation
  • 6.6 Observer Design for the Ginzburg-Landau Equation 98
  • 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
  • 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
  • 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
  • 8.1 Plant with Unknown Reaction Coefficient
  • 8.2 Proof of Theorem
  • 8.3 Well-Posedness of the Closed-Loop System
  • 8.4 Parametric Robustness
  • 8.5 An Alternative Approach
  • 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
  • 9.1 Benchmark Plant
  • 9.2 3D Reaction-Advection-Diffusion Plant
  • 9.3 Proof of Theorem
  • 9.4 Simulations
  • 9.5 Notes and References
  • 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
  • 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
  • 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
  • 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
  • 12.4 Swapping Design--Plant with Unknown Parameter in the Boundary Condition
  • 12.5 Simulations
  • 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
  • 13.4 Filters
  • 13.5 Frequency Domain Compensator with Frozen Parameters
  • 13.6 Update Laws
  • 13.7 Stability
  • 13.8 Trajectory Tracking
  • 13.9 The 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
  • 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
  • 14.5 Comparison with the LQR Approach
  • 14.6 Inverse Optimal Adaptive Control
  • 14.7 Stability and Inverse Optimality of the Adaptive Scheme
  • Appendix A. Adaptive Backstepping for Nonlinear ODEs--The Basics
  • 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
  • Appendix B. Poincaré and Agmon Inequalities
  • Appendix C. Bessel Functions
  • C.1 Bessel Function
  • C.2 Modified Bessel Function In
  • Appendix D. Barbalat's and Other Lemmas for Proving Adaptive Regulation
  • 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

Podobne zapisy