Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations

Häftad, Engelska, 2018

Av Alexander Y. Khapalov

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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.

Produktinformation

Utgivningsdatum2018-08-11
Mått155 x 235 x 14 mm
Vikt388 g
FormatHäftad
SpråkEngelska
Antal sidor233
FörlagSpringer International Publishing AG
ISBN9783319868592

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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.

“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)