Adaptive control of parabolic PDEs / Andrey Smyshlyaevand Miroslav Krstic.

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 also ...

Includes bibliographical references and index.

Introduction -- Nonadaptive controllers. State feedback -- Closed-form controllers -- Observers -- Output feedback -- Control of complex-valued PDEs -- Adaptive schemes. Systemization of approaches to adaptive boundary stabilization of PDEs -- Lyapunov-based designs -- Certainty equivalence design with passive identifiers -- Certainty equivalence design with swapping identifiers -- State feedback for PDEs with spatially varying coefficients -- Closed-form adaptive output-feedback controllers -- Output feedback for PDEs with spatially varying coefficients -- Inverse optimal control -- Appendex A. Adaptive backstepping for nonlinear ODEs -- the basics -- Appendix B. Poincaré and Agmon inequalities -- Appendix C. Bessel functions -- Appendix D. Barbalat's and other lemmas for proving adaptive regulation -- Appendix E. Basic parabolic PDEs and their exact solution.

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