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Observation andControl for OperatorSemigroups Marius TucsnakGeorge H. Weiss2009 год

Observation and Control for Operator Semigroups
книга

Страница публикацииПубликация в OpenAlex
Аннотация: The evolution of the state of many systems modeled by linear partial difierentialequations (PDEs) or linear delay-difierential equations can be described by operatorsemigroups. The state of such a system is an element in an inflnite-dimensionalnormed space, whence the name \inflnite-dimensional linear system.The study of operator semigroups is a mature area of functional analysis, which isstill very active. The study of observation and control operators for such semigroupsis relatively more recent. These operators are needed to model the interactionof a system with the surrounding world via outputs or inputs. The main topicsof interest about observation and control operators are admissibility, observability,controllability, stabilizability and detectability. Observation and control operatorsare an essential ingredient of well-posed linear systems (or more generally systemnodes). Inthisbookwedealonlywithadmissibility, observabilityandcontrollability.We deal only with operator semigroups acting on Hilbert spaces.This book is meant to be an elementary introduction into the topics mentionedabove. By \elementary we mean that we assume no prior knowledge of flnite-dimensional control theory, and no prior knowledge of operator semigroups or ofunbounded operators. We introduce everything needed from these areas. We doassume that the reader has a basic understanding of bounded operators on Hilbertspaces, difierential equations, Fourier and Laplace transforms, distributions andSobolev spaces on
Год издания: 2009
Авторы: Marius Tucsnak, George H. Weiss
Источник: Birkhäuser Basel eBooks
Ключевые слова: Stability and Controllability of Differential Equations, Advanced Mathematical Modeling in Engineering, Numerical methods in inverse problems
Другие ссылки: Birkhäuser Basel eBooks (HTML)
HAL (Le Centre pour la Communication Scientifique Directe) (HTML)
HAL (Le Centre pour la Communication Scientifique Directe) (HTML)