关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

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

Observation and Control for Operator Semigroups

This book presents methods to study the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions. The emphasis is put on specific phenomena due to nonlinearities. In particular, many examples are given where nonlinearities turn out to be essential to get controllability or stabilization. Various methods are presented to study the controllability or to construct stabilizing feedback laws. The power of these methods is illustrated by numerous examples coming from such areas as celestial mechanics, fluid mechanics, and quantum mechanics. The book is addressed to graduate students in mathematics or control theory, and to mathematicians or engineers with an interest in nonlinear control systems governed by ordinary or partial differential equations.

/pdf/control-and-nonlinearity-4tu8aduvuy.pdf

Control and Nonlinearity

Convex Analysis: (pms-28)

Linear Evolutionary Problems Hidden Regularity Weak Solutions Uniqueness Theorems Exact Controllability Hilbert Uniqueness Method Norm Inequalities New Uniqueness and Exact Controllability Results Dissipative Evolutionary Systems Linear Stabilization Nonlinear Stabilization Internal Stabilization of the Korteweg-de Vries Equation.

/pdf/exact-controllability-and-stabilization-the-multiplier-2obtftnarf.pdf

Exact controllability and stabilization: The multiplier method

A direct method for the boundary stabilization of the wave equation

This book uses techniques of Fourier series and functional analysis to deal with certain problems in differential equations The Fourier series and functional analysis are merely tools; the authors' real interest lies in the differential equations that they study It has been known since 1967 that a wide variety of sets {ewikt} of complex exponential functions play an important role in the control theory of systems governed by partial differential equations However, this book is the first serious attempt to gather all of the available theory of these "nonharmonic Fourier series" in one place, combining published results with new results by the authors, to create a unique source of such material for practicing applied mathematicians, engineers and other scientific professionals

Fourier Series in Control Theory

/pdf/characterization-of-the-unique-expansions-1-sum-infty-i-1-q-lwui7ppu6y.pdf

Characterization of the unique expansions $1=\sum ^{\infty }_{i=1}q^{-n_ i}$ and related problems

https://www.mat.univie.ac.at/%7Eesiprpr/esi1810.pdf

Vilmos Komornik

Papers

Exact controllability and stabilization: The multiplier method

A direct method for the boundary stabilization of the wave equation

Fourier Series in Control Theory

Characterization of the unique expansions $1=\sum ^{\infty }_{i=1}q^{-n_ i}$ and related problems

Unique expansions of real numbers