Control of Wave and Beam PDEs

The Riesz Basis Approach

Nonfiction, Science & Nature, Mathematics, Differential Equations, Technology, Automation
Cover of the book Control of Wave and Beam PDEs by Bao-Zhu Guo, Jun-Min Wang, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Bao-Zhu Guo, Jun-Min Wang ISBN: 9783030124816
Publisher: Springer International Publishing Publication: March 28, 2019
Imprint: Springer Language: English
Author: Bao-Zhu Guo, Jun-Min Wang
ISBN: 9783030124816
Publisher: Springer International Publishing
Publication: March 28, 2019
Imprint: Springer
Language: English

Control of Wave and Beam PDEs is a concise, self-contained introduction to Riesz bases in Hilbert space and their applications to control systems described by partial differential equations (PDEs). The authors discuss classes of systems that satisfy the spectral determined growth condition, the problem of stability, and the relationship between fulfillment of the condition and stability.

Using the (fundamental) Riesz-basis property, the book shows how controllability, observability, stability, etc., can be derived for a linear system. The text provides a crash course in the mathematical theory of Riesz bases so that a reader can quickly understand this powerful method of dealing with linear PDEs. It introduces several important methods for achieving the Riesz basis property through spectral analysis, as well as new approaches including treatment of systems coupled through boundary weak connections.

The book moves from a discussion of mathematical preliminaries through bases in Hilbert Spaces to applications to Euler–Bernoulli and Rayleigh beam equations and hybrid systems. The final chapter expands the use of the book’s methods to applications in other systems.

Many typical examples, representing physical systems, are discussed in the text. The book is suitable not only for applied mathematicians seeking a powerful tool to understand control systems, but also for control engineers interested in the mathematics of PDE systems.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Control of Wave and Beam PDEs is a concise, self-contained introduction to Riesz bases in Hilbert space and their applications to control systems described by partial differential equations (PDEs). The authors discuss classes of systems that satisfy the spectral determined growth condition, the problem of stability, and the relationship between fulfillment of the condition and stability.

Using the (fundamental) Riesz-basis property, the book shows how controllability, observability, stability, etc., can be derived for a linear system. The text provides a crash course in the mathematical theory of Riesz bases so that a reader can quickly understand this powerful method of dealing with linear PDEs. It introduces several important methods for achieving the Riesz basis property through spectral analysis, as well as new approaches including treatment of systems coupled through boundary weak connections.

The book moves from a discussion of mathematical preliminaries through bases in Hilbert Spaces to applications to Euler–Bernoulli and Rayleigh beam equations and hybrid systems. The final chapter expands the use of the book’s methods to applications in other systems.

Many typical examples, representing physical systems, are discussed in the text. The book is suitable not only for applied mathematicians seeking a powerful tool to understand control systems, but also for control engineers interested in the mathematics of PDE systems.

More books from Springer International Publishing

Cover of the book Modeling, Dynamics, Optimization and Bioeconomics II by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Recent Trends in Applied Nonlinear Mechanics and Physics by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Nanomaterials and Plant Potential by Bao-Zhu Guo, Jun-Min Wang
Cover of the book A History of the Solar System by Bao-Zhu Guo, Jun-Min Wang
Cover of the book The Politics of Contaminated Sites Management by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Dynamic Spectrum Access for Wireless Networks by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Foundations of Augmented Cognition by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Spin Dynamics and Damping in Ferromagnetic Thin Films and Nanostructures by Bao-Zhu Guo, Jun-Min Wang
Cover of the book FlexSim in Academe: Teaching and Research by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Tissue Engineering for the Heart by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Homological and Computational Methods in Commutative Algebra by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Insects, Fire and Conservation by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Selected Areas in Cryptography -- SAC 2014 by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Applications of Soft Computing in Time Series Forecasting by Bao-Zhu Guo, Jun-Min Wang
Cover of the book The SAGES Manual Ethics of Surgical Innovation by Bao-Zhu Guo, Jun-Min Wang
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy