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This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time. Based on the author's extensive research in the area of controllability theory, this monograph specifically focuses on the issues of controllability, observability, and stabilizability for parabolic and hyperbolic partial differential equations. The topics in this book also cover related applied questions such as the problem of localization of unknown pollution sources based on information obtained from point sensors that arise in environmental monitoring. Researchers and graduate students interested in controllability theory of partial differential equations and its applications will find this book to be an invaluable resource to their studies.
List of contents
1. Introduction.- Part I: 2. Continuous observability of the heat equation under a single mobile point sensor.- 3. Continuous observability of the 2-nd order paragolic equations under degenerate mobile sensors.- Part II: 4. Behavior of solutions of the semilinear heat equation in vanishing time and controllability.- 5. Controllability of the semiliniear heat equation with sublinear term and degenerate actuator.- 6. Controllability of the semilinear reaction-diffusion equation with degenerate actuator.- 7. Semilinear parabolic equations: Mobile point controls vs the locally distributed ones.- Part III: 8. Degenerate sensors in source localization and sensor placement problems.- Part IV: 9. Continuous observability of hyperbolic equations under degenerate sensors.- 10. Controllability of the wave equation governed by mobile point controls.- Part V: 11. Exponential decay for the wave equation equipped with a point damping device.- 12. A vibrating string with shuttle-like point dampers andrelated observability properties.- References.
About the author
Alexander Y. Khapalov is a professor in the Department of Mathematics at Washington State University.
Summary
This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time. Based on the author’s extensive research in the area of controllability theory, this monograph specifically focuses on the issues of controllability, observability, and stabilizability for parabolic and hyperbolic partial differential equations. The topics in this book also cover related applied questions such as the problem of localization of unknown pollution sources based on information obtained from point sensors that arise in environmental monitoring. Researchers and graduate students interested in controllability theory of partial differential equations and its applications will find this book to be an invaluable resource to their studies.
Additional text
“The monograph under review constitutes an extremely valuable contribution to the research related to pointwise sensors and actuators, both static and mobile. It has been written by a renowned expert in this extremely challenging area. … it is accessible to graduate students in applied mathematics, engineering and physics. Due to mathematical rigor, its reading is also recommended to more advance practitioners who aim at implementing control or observation strategies using mobile sensors or actuators.” (Dariusz Uciński, Mathematical reviews, September, 2018)
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"The monograph under review constitutes an extremely valuable contribution to the research related to pointwise sensors and actuators, both static and mobile. It has been written by a renowned expert in this extremely challenging area. ... it is accessible to graduate students in applied mathematics, engineering and physics. Due to mathematical rigor, its reading is also recommended to more advance practitioners who aim at implementing control or observation strategies using mobile sensors or actuators." (Dariusz Ucinski, Mathematical reviews, September, 2018)
