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Conceived by Count Jacopo Francesco Riccati more than a quarter of
a millennium ago, the Riccati equation has been widely studied in
the subsequent centuries. Since its introduction in control theory
in the sixties, the matrix Riccati equation has known an impressive
range of applications, such as optimal control, H? optimization and
robust stabilization, stochastic realization, synthesis of linear
passive networks, to name but a few. This book consists of 11
chapters surveying the main concepts and results related to the
matrix Riccati equation, both in continuous and discrete time.
Theory, applications and numerical algorithms are extensively
presented in an expository way. As a foreword, the history and
prehistory of the Riccati equation is concisely presented.
The problem of obtaining dynamical models directly from an observed
time-series occurs in many fields of application. There are a
number of possible approaches to this problem. In this volume a
number of such points of view are exposed: the statistical time
series approach, a theory of guaranted performance, and finally a
deterministic approximation approach. This volume is an out-growth
of a number of get-togethers sponsered by the Systems and Decision
Sciences group of the International Institute of Applied Systems
Analysis (IIASA) in Laxenburg, Austria. The hospitality and support
of this organization is gratefully acknowledged. Jan Willems
Groningen, the Netherlands May 1989 TABLE OF CONTENTS Linear System
Identification- A Survey page 1 M. Deistler A Tutorial on
Hankel-Norm Approximation 26 K. Glover A Deterministic Approach to
Approximate Modelling 49 C. Heij and J. C. Willems Identification -
a Theory of Guaranteed Estimates 135 A. B. Kurzhanski Statistical
Aspects of Model Selection 215 R. Shibata Index 241 Addresses of
Authors 246 LINEAR SYSTEM IDENTIFICATION* A SURVEY M. DEISTLER
Abstract In this paper we give an introductory survey on the theory
of identification of (in general MIMO) linear systems from
(discrete) time series data. The main parts are: Structure theory
for linear systems, asymptotic properties of maximum likelihood
type estimators, estimation of the dynamic specification by methods
based on information criteria and finally, extensions and
alternative approaches such as identification of unstable systems
and errors-in-variables. Keywords Linear systems, parametrization,
maximum likelihood estimation, information criteria,
errors-in-variables.
System and Control theory is one of the most exciting areas of
contemporary engineering mathematics. From the analysis of Watt's
steam engine governor - which enabled the Industrial Revolution -
to the design of controllers for consumer items, chemical plants
and modern aircraft, the area has always drawn from a broad range
of tools. It has provided many challenges and possibilities for
interaction between engineering and established areas of 'pure' and
'applied' mathematics. This impressive volume collects a discussion
of more than fifty open problems which touch upon a variety of
subfields, including: chaotic observers, nonlinear local
controlability, discrete event and hybrid systems, neural network
learning, matrix inequalities, Lyapunov exponents, and many other
issues. Proposed and explained by leading researchers, they are
offered with the intention of generating further work, as well as
inspiration for many other similar problems which may naturally
arise from them. With extensive references, this book will be a
useful reference source - as well as an excellent addendum to the
textbooks in the area.
This is a collection of articles by friends, co-authors,
colleagues, and students of Keith Glover, Professor of Engineering
at the University of Cambridge, on the occasion of his 60th
birthday. Professor Glover's work spans a variety of topics,
including system identification, model reduction and approximation,
robust controller synthesis, and control of aircraft and engines.
The collection is a tribute to Professor Glover's seminal work in
these areas.
Conceived by Count Jacopo Francesco Riccati more than a quarter of
a millennium ago, the Riccati equation has been widely studied in
the subsequent centuries. Since its introduction in control theory
in the sixties, the matrix Riccati equation has known an impressive
range of applications, such as optimal control, H? optimization and
robust stabilization, stochastic realization, synthesis of linear
passive networks, to name but a few. This book consists of 11
chapters surveying the main concepts and results related to the
matrix Riccati equation, both in continuous and discrete time.
Theory, applications and numerical algorithms are extensively
presented in an expository way. As a foreword, the history and
prehistory of the Riccati equation is concisely presented.
This book contains the text of the plenary lectures and the
mini-courses of the European Control Conference (ECC'93) held in
Groningen, the Netherlands, June 2S-July 1, 1993. However, the book
is not your usu al conference proceedings. Instead, the authors
took this occasion to take a broad overview of the field of control
and discuss its development both from a theoretical as well as from
an engineering perpective. The first essay is by the key-note
speaker ofthe conference, A.G.J. Mac Farlane. It consists of a
non-technical discussion of information processing and knowledge
acquisition as the key features of control engineering tech nology.
The next six articles are accounts of the plenary addresses. The
contribution by R.W. Brockett concerns a mathematical framework for
modelling motion control, a central question in robotics and
vision. In the paper by M. Morari the engineering and the economic
relevance of chemical process control are considered, in particular
statistical quality control and the control of systems with
constraints. The article by A.C.P.M. Backx is written from an
industrial perspec tive. The author is director of an engineering
consulting firm involved in the design of industrial control
equipment. Specifically, the possibility of obtaining high
performance and reliable controllers by modelling, identifi cation,
and optimizing industrial processes is discussed.
This Festschrift, published on the occasion of the sixtieth
birthday of Yutaka - mamoto ('YY' as he is occasionally casually
referred to), contains a collection of articles by friends,
colleagues, and former Ph.D. students of YY. They are a tribute to
his friendship and his scienti?c vision and oeuvre, which has been
a source of inspiration to the authors. Yutaka Yamamoto was born in
Kyoto, Japan, on March 29, 1950. He studied applied mathematics and
general engineering science at the Department of Applied
Mathematics and Physics of Kyoto University, obtaining the B.S. and
M.Sc. degrees in 1972 and 1974. His M.Sc. work was done under the
supervision of Professor Yoshikazu Sawaragi. In 1974, he went to
the Center for Mathematical System T- ory of the University of
Florida in Gainesville. He obtained the M.Sc. and Ph.D. degrees,
both in Mathematics, in 1976 and 1978, under the direction of
Professor Rudolf Kalman.
Exact and Approximate Modelling of Linear Systems: A Behavioural
Approach elegantly introduces the behavioural approach to
mathematical modelling, an approach that requires models to be
viewed as sets of possible outcomes rather than to be a priori
bound to particular representations. The authors discuss exact and
approximate fitting of data by linear, bilinear, and quadratic
static models and linear dynamic models, a formulation that enables
readers to select the most suitable representation for a particular
purpose. This book presents exact subspace-type and approximate
optimization-based identification methods, as well as
representation-free problem formulations, an overview of solution
approaches, and software implementation. Readers will find an
exposition of a wide variety of modelling problems starting from
observed data. The presented theory leads to algorithms that are
implemented in C language and in MATLAB.
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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