Nonlinear and Robust Control of PDE Systems

1 Introduction.- 1.1 Motivation.- 1.2 Examples of Transport-Reaction Processes.- 1.3 Background on Control of PDE Systems.- 1.4 Objectives and Organization of the Book.- 2 Feedback Control of Hyperbolic PDE Systems.- 2.1 Introduction.- 2.2 First-Order Hyperbolic PDE Systems.- 2.3 Characteristic Index.- 2.4 State Feedback Control.- 2.5 Closed-Loop Stability.- 2.6 Output Feedback Control.- 2.7 Application to a Nonisothermal Plug-Flow Reactor.- 2.8 Conclusions.- 3 Robust Control of Hyperbolic PDE Systems.- 3.1 Introduction.- 3.2 Preliminaries.- 3.3 Uncertainty Decoupling.- 3.4 Robust Control: Uncertain Variables.- 3.5 Two-Time-Scale Hyperbolic PDE Systems.- 3.6 Robustness with Respect to Unmodeled Dynamics.- 3.7 Application to a Fixed-Bed Reactor.- 3.8 Conclusions.- 4 Feedback Control of Parabolic PDE Systems.- 4.1 Introduction.- 4.2 Preliminaries.- 4.3 Examples of Processes Modeled by Nonlinear Parabolic PDEs.- 4.4 Galerkin’s Method.- 4.5 Accuracy of ODE System Obtained From Galerkin’s Method.- 4.6 Construction of ODE Systems of Desired Accuracy via AIMs.- 4.7 Nonlinear Output Feedback Control.- 4.8 Applications.- 4.9 Conclusions.- 5 Robust Control of Parabolic PDE Systems.- 5.1 Introduction.- 5.2 Preliminaries.- 5.3 Robust State Feedback Control of Parabolic PDE Systems.- 5.4 Robust Output Feedback Controller Synthesis.- 5.5 Application to a Catalytic Rod with Uncertainty.- 5.6 Conclusions.- 6 Nonlinear and Robust Control of Parabolic PDE Systems with Time-Dependent Spatial Domains.- 6.1 Introduction.- 6.2 Preliminaries.- 6.3 Nonlinear Model Reduction.- 6.4 Nonlinear Output Feedback Control.- 6.5 Application to a Catalytic Rod with Moving Boundary.- 6.6 Robust Control of Parabolic PDEs with Time-Dependent Spatial Domains.- 6.7 Application to a Catalytic Rod withMoving Boundary and Uncertainty.- 6.8 Conclusions.- 7 Case Studies.- 7.1 Nonlinear Control of Rapid Thermal Chemical Vapor Deposition.- 7.2 Nonlinear Control of Czochralski Crystal Growth.- 7.3 Conclusions.- Appendix A: Proofs of Chapter 2.- Appendix B: Proofs of Chapter 3.- Appendix C: Proofs of Chapter 4.- Appendix D: Proofs of Chapter 5.- Appendix E: Proofs of Chapter 6.- Appendix F: Karhunen-Loève Expansion.- References.