| Elementary Feedback Stabilization of the Linear Reaction-Convection-Diffusion Equation and the Wave Equation 2010 Edition Contributor(s): Liu, Weijiu (Author) |
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ISBN: 3642046126 ISBN-13: 9783642046124 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: December 2009 |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - General - Mathematics | Applied - Technology & Engineering | Automation |
| Dewey: 629.831 |
| Series: Matha(c)Matiques Et Applications |
| Physical Information: 0.65" H x 6.14" W x 9.21" (0.96 lbs) 296 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |
