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 Climate Change Adaptation, Resilience and Hazards by Bao-Zhu Guo, Jun-Min Wang
Cover of the book A Tissue Regeneration Approach to Bone and Cartilage Repair by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Electronic Control Fires by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Problem Behavior Theory and the Social Context by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Nearly Zero Energy Communities by Bao-Zhu Guo, Jun-Min Wang
Cover of the book The Palgrave Handbook of Affect Studies and Textual Criticism by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Growing up Working Class by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Ecotourism’s Promise and Peril by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Theory and Applications of Formal Argumentation by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Cultural, Autobiographical and Absent Memories of Orphanhood by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Dynamic Modeling, Empirical Macroeconomics, and Finance by Bao-Zhu Guo, Jun-Min Wang
Cover of the book The Politics of Healthcare Reform in Turkey by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Nonlinear Dynamics New Directions by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Computational Red Teaming by Bao-Zhu Guo, Jun-Min Wang
Cover of the book Historical Earthquake-Resistant Timber Framing in the Mediterranean Area 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