Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations / by Alexander Y. Khapalov.

Format:

Book

Author/Creator:

Khapalov, Alexander Y., Author.

Language:

English

Subjects (All):

Differential equations, Partial.

System theory.

Partial Differential Equations.

Systems Theory, Control.

Local Subjects:

Partial Differential Equations.

Systems Theory, Control.

Physical Description:

1 online resource (XVI, 233 p. 11 illus.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

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.

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. .

Notes:

Includes bibliographical references and index.

ISBN:

3-319-60414-7