Elementary Feedback Stabilization of the Linear Reaction-Convection-Diffusion Equation and the Wave Equation
Springer Berlin (Verlag)
978-3-642-04612-4 (ISBN)
Mathematical control theory of applied partial differential equations is built on linear andnonlinearfunctionalanalysisand manyexistencetheoremsin controlt- ory result from applications of theorems in functional analysis. This makes control theoryinaccessibleto studentswhodo nothave a backgroundin functionalanalysis. Many advanced control theory books on in?nite-dimensionalsystems were wr- ten, using functional analysis and semigroup theory, and control theory was p- sented in an abstract setting. This motivates me to write this text for control theory classes in the way to present control theory by concrete examples and try to m- imize the use of functional analysis. Functional analysis is not assumed and any analysis included here is elementary, using calculus such as integration by parts. The material presented in this text is just a simpli?cation of the material from the existing advanced control books. Thus this text is accessible to senior undergra- ate studentsand?rst-yeargraduatestudentsin appliedmathematics,who havetaken linear algebra and ordinary and partial differential equations. Elementary functional analysis is presented in Chapter 2. This material is - quired to present the control theory of partial differential equations. Since many control conceptsand theories for partial differentialequations are transplanted from ?nite-dimensionalcontrol systems, a brief introduction to feedback control of these systemsispresentedinChapter3.Thetopicscoveredinthischapterincludecontr- lability, observability,stabilizability, pole placement, and quadratic optimal control.
Examples of Control Systems.- Elementary Functional Analysis.- Finite Dimensional Systems.- Linear Reaction-Convection-Diffusion Equation.- One-dimensional Wave Equation.- Higher-dimensional Wave Equation.
From the reviews:
"This book is an introduction to the mathematical control theory of some applied partial differential equations. ... The material in this book is a nice simplification of that from the existing advanced monographs on infinite-dimensional control theory. ... This text can be used as a textbook for a one-semester graduate course on control theory for the systems governed by partial differential equations." (Xu Zhang, Mathematical Reviews, Issue 2010 m)
"This book is an introductory text in control theory of partial differential equations (PDEs) intended for first-year graduate students in mathematics or engineering ... . book is well thought out and the topics flow together nicely. ... This textbook would be very suitable as a primary text for a course on control theory of PDEs that emphasizes application of feedback stabilization theory to concrete PDEs. ... also serve as a valuable side reference in a more general or abstract course with its many excellent examples." (Scott W. Hansen, SIAM Review, Vol. 53 (2), 2011)
| Erscheint lt. Verlag | 15.12.2009 |
|---|---|
| Reihe/Serie | Mathématiques et Applications |
| Zusatzinfo | X, 296 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 960 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Technik ► Elektrotechnik / Energietechnik | |
| Schlagworte | Control Theory • integral transform • optimal control • partial differential equation • Partial differential equations • wave equation |
| ISBN-10 | 3-642-04612-6 / 3642046126 |
| ISBN-13 | 978-3-642-04612-4 / 9783642046124 |
| Zustand | Neuware |
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