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The present volume comprises survey articles on various fields of
Differential-Algebraic Equations (DAEs) which have widespread
applications in controlled dynamical systems, especially in
mechanical and electrical engineering and a strong relation to
(ordinary) differential equations. The individual chapters provide
reviews, presentations of the current state of research and new
concepts in - History of DAEs - DAE aspects of mechanical multibody
systems - Model reduction of DAEs - Observability for DAEs -
Numerical Analysis for DAEs The results are presented in an
accessible style, making this book suitable not only for active
researchers but also for graduate students (with a good knowledge
of the basic principles of DAEs) for self-study.
The present volume comprises survey articles on various fields of
Differential-Algebraic Equations (DAEs), which have widespread
applications in controlled dynamical systems, especially in
mechanical and electrical engineering and a strong relation to
(ordinary) differential equations. The individual chapters provide
reviews, presentations of the current state of research and new
concepts in - Flexibility of DAE formulations - Reachability
analysis and deterministic global optimization - Numerical linear
algebra methods - Boundary value problems The results are presented
in an accessible style, making this book suitable not only for
active researchers but also for graduate students (with a good
knowledge of the basic principles of DAEs) for self-study.
The present volume comprises survey articles on various fields of
Differential-Algebraic Equations (DAEs), which have widespread
applications in controlled dynamical systems, especially in
mechanical and electrical engineering and a strong relation to
(ordinary) differential equations. The individual chapters provide
reviews, presentations of the current state of research and new
concepts in - Observers for DAEs - DAEs in chemical processes -
Optimal control of DAEs - DAEs from a functional-analytic viewpoint
- Algebraic methods for DAEs The results are presented in an
accessible style, making this book suitable not only for active
researchers but also for graduate students (with a good knowledge
of the basic principles of DAEs) for self-study.
The need for a rigorous mathematical theory for
Differential-Algebraic Equations (DAEs) has its roots in the
widespread applications of controlled dynamical systems, especially
in mechanical and electrical engineering. Due to the strong
relation to (ordinary) differential equations, the literature for
DAEs mainly started out from introductory textbooks. As such, the
present monograph is new in the sense that it comprises survey
articles on various fields of DAEs, providing reviews,
presentations of the current state of research and new concepts in
- Controllability for linear DAEs - Port-Hamiltonian
differential-algebraic systems - Robustness of DAEs - Solution
concepts for DAEs - DAEs in circuit modeling. The results in the
individual chapters are presented in an accessible style, making
this book suitable not only for active researchers but also for
graduate students (with a good knowledge of the basic principles of
DAEs) for self-study.
Over the last decade the field of adaptive control where no
identification mechanisms are invoked has become a major research
topic. This book presents a state-of-the-art report on the
following more specific area: the system classes under
consideration contain linear (possibly nonlinearly perturbed),
finite dimensional, continuous time systems which are stabilizable
by high-gain output feedback. The properties of minimum phase
systems and strictly positive real systems are studied in their own
right. These results are applied to design simple adaptive
controllers involving a switching strategy which is mainly tuned by
a one parameter controller based on output data alone. Control
objectives are stabilization, tracking, -tracking and
servomechanism action. In addition, robustness with respect to
nonlinear perturbations and performance improvements are
investigated.
This volume encompasses prototypical, innovative and emerging
examples and benchmarks of Differential-Algebraic Equations (DAEs)
and their applications, such as electrical networks, chemical
reactors, multibody systems, and multiphysics models, to name but a
few. Each article begins with an exposition of modelling,
explaining whether the model is prototypical and for which
applications it is used. This is followed by a mathematical
analysis, and if appropriate, a discussion of the numerical aspects
including simulation. Additionally, benchmark examples are included
throughout the text. Mathematicians, engineers, and other
scientists, working in both academia and industry either on
differential-algebraic equations and systems or on problems where
the tools and insight provided by differential-algebraic equations
could be useful, would find this book resourceful.
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