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Loosely speaking, adaptive systems are designed to deal with, to
adapt to, chang ing environmental conditions whilst maintaining
performance objectives. Over the years, the theory of adaptive
systems evolved from relatively simple and intuitive concepts to a
complex multifaceted theory dealing with stochastic, nonlinear and
infinite dimensional systems. This book provides a first
introduction to the theory of adaptive systems. The book grew out
of a graduate course that the authors taught several times in
Australia, Belgium, and The Netherlands for students with an
engineering and/or mathemat ics background. When we taught the
course for the first time, we felt that there was a need for a
textbook that would introduce the reader to the main aspects of
adaptation with emphasis on clarity of presentation and precision
rather than on comprehensiveness. The present book tries to serve
this need. We expect that the reader will have taken a basic course
in linear algebra and mul tivariable calculus. Apart from the basic
concepts borrowed from these areas of mathematics, the book is
intended to be self contained."
Loosely speaking, adaptive systems are designed to deal with, to
adapt to, chang ing environmental conditions whilst maintaining
performance objectives. Over the years, the theory of adaptive
systems evolved from relatively simple and intuitive concepts to a
complex multifaceted theory dealing with stochastic, nonlinear and
infinite dimensional systems. This book provides a first
introduction to the theory of adaptive systems. The book grew out
of a graduate course that the authors taught several times in
Australia, Belgium, and The Netherlands for students with an
engineering and/or mathemat ics background. When we taught the
course for the first time, we felt that there was a need for a
textbook that would introduce the reader to the main aspects of
adaptation with emphasis on clarity of presentation and precision
rather than on comprehensiveness. The present book tries to serve
this need. We expect that the reader will have taken a basic course
in linear algebra and mul tivariable calculus. Apart from the basic
concepts borrowed from these areas of mathematics, the book is
intended to be self contained."
This is a book about modelling, analysis and control of linear
time- invariant systems. The book uses what is called the
behavioral approach towards mathematical modelling. Thus a system
is viewed as a dynamical relation between manifest and latent
variables. The emphasis is on dynamical systems that are
represented by systems of linear constant coefficients. In the
first part of the book the structure of the set of trajectories
that such dynamical systems generate is analyzed. Conditions are
obtained for two systems of differential equations to be equivalent
in the sense that they define the same behavior. It is further
shown that the trajectories of such linear differential systems can
be partitioned in free inputs and bound outputs. In addition the
memory structure of the system is analyzed through state space
models. The second part of the book is devoted to a number of
important system properties, notably controllability,
observability, and stability. An essential feature of using the
behavioral approach is that it allows these and similar concepts to
be introduced in a representation-free manner. In the third part
control problems are considered, more specifically stabilization
and pole placement questions. This text is suitable for advanced
undergraduate or beginning graduate students in mathematics and
engineering. It contains numerous exercises, including simulation
problems, and examples, notably of mechanical systems and
electrical circuits.
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