Cover -- Title -- Copyright -- Contents -- Preface -- 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 Schrödinger Equation -- 6.2 Observer Design for the Schrödinger Equation.

6.3 Output-Feedback Compensator for the Schrödinger 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 -- 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 8.1 -- 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 9.2 -- 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 Parameter in the Domain -- 12.4 Swapping Design-Plant with Unknown Parameter in the Boundary Condition -- 12.5 Simulations -- 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 -- 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 -- 13.13 Notes and References -- 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 -- 14.8 Notes and References -- 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 J[sub(n)] -- C.2 Modified Bessel Function I[sub(n)] -- 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 -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W.