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

• Main Author: Khapalov, Alexander Y. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Subjects: Mathematics.; Partial differential equations.; System theory.; Partial Differential Equations.; Systems Theory, Control.

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 spec...

Table 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 and related observability properties
• References. .