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This concise and highly usable textbook presents an introduction to backstepping, an elegant new approach to boundary control of partial differential equations (PDEs). Backstepping provides mathematical tools for converting complex and unstable PDE into elementary, stable, and physically intuitive target PDE systems that are familiar to engineers and physicists. The text s broad coverage includes parabolic PDEs; hyperbolic PDEs of first and second order; fluid, thermal, and structural systems; delay systems; PDEs with third and fourth derivatives in space; real-valued as well as complex-valued PDEs; stabilization as well as motion planning and trajectory tracking for PDEs; and elements of adaptive control for PDEs and control of nonlinear PDEs. It is appropriate for courses in control theory and includes homework exercises and a solutions manual that is available from the authors upon request. Audience: This book is intended for both beginning and advanced graduate students in a one-quarter or one-semester course on backstepping techniques for boundary control of PDEs. It is also accessible to engineers with no prior training in PDEs. Contents: List of Figures; List of Tables; Preface; Introduction; Lyapunov Stability; Exact Solutions to PDEs; Parabolic PDEs: Reaction-Advection-Diffusion and Other Equations; Observer Design; Complex-Valued PDEs: Schrodinger and Ginzburg Landau Equations; Hyperbolic PDEs: Wave Equations; Beam Equations; First-Order Hyperbolic PDEs and Delay Equations; Kuramoto Sivashinsky, Korteweg de Vries, and Other Exotic Equations; Navier Stokes Equations; Motion Planning for PDEs; Adaptive Control for PDEs; Towards Nonlinear PDEs; Appendix: Bessel Functions; Bibliography; Index
Miroslav Krstić (Tue,) studied this question.