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Fuzzy controllers are a class of knowledge based controllers using
artificial intelligence techniques with origins in fuzzy logic.
They can be found either as stand-alone control elements or as
integral parts of a wide range of industrial process control
systems and consumer products. Applications of fuzzy controllers
are an established practice for Japanese manufacturers, and are
spreading in Europe and America. The main aim of this book is to
show that fuzzy control is not totally ad hoc, that there exist
formal techniques for the analysis of a fuzzy controller, and that
fuzzy control can be implemented even when no expert knowledge is
available. The book is mainly oriented to control engineers and
theorists, although parts can be read without any knowledge of
control theory and may interest AI people. This 2nd, revised
edition incorporates suggestions from numerous reviewers and
updates and reorganizes some of the material.
Fuzzy controllers are a class of knowledge based controllers using
artificial intelligence techniques with origins in fuzzy logic.
They can be found either as stand-alone control elements or as
integral parts of distributed control systems including
conventional controllers in a wide range of industrial process
control systems and consumer products. Applications of fuzzy
controllers have become a well established practice for Japanese
manufacturers of control equipment and systems, and are becoming
more and more common in Europe and America. The main aim of this
book is to show that fuzzy control is not totally ad hoc, that
there exist formal techniques for the analysis of a fuzzy
controller, and that fuzzy control can be implemented even when no
expert knowledge is available. Thus the book is mainly oriented
toward control engineers and theorists, although parts can be read
without any knowledge of control theory and may be of interest to
Al people. This 2nd, revised edition incorporates suggestions from
numerous reviewers and updates and reorganizes some of the
material.
The DMV seminar "Stochastische Approximation und Optimierung
zufalliger Systeme" was held at Blaubeuren, 28. 5. -4. 6. 1989. The
goal was to give an approach to theory and application of stochas
tic approximation in view of optimization problems, especially in
engineering systems. These notes are based on the seminar lectures.
They consist of three parts: I. Foundations of stochastic
approximation (H. Walk); n. Applicational aspects of stochastic
approximation (G. PHug); In. Applications to adaptation: ugorithms
(L. Ljung). The prerequisites for reading this book are basic
knowledge in probability, mathematical statistics, optimization. We
would like to thank Prof. M. Barner and Prof. G. Fischer for the or
ganization of the seminar. We also thank the participants for their
cooperation and our assistants and secretaries for typing the
manuscript. November 1991 L. Ljung, G. PHug, H. Walk Table of
contents I Foundations of stochastic approximation (H. Walk) 1
Almost sure convergence of stochastic approximation procedures 2 2
Recursive methods for linear problems 17 3 Stochastic optimization
under stochastic constraints 22 4 A learning model; recursive
density estimation 27 5 Invariance principles in stochastic
approximation 30 6 On the theory of large deviations 43 References
for Part I 45 11 Applicational aspects of stochastic approximation
(G. PHug) 7 Markovian stochastic optimization and stochastic
approximation procedures 53 8 Asymptotic distributions 71 9
Stopping times 79 1O Applications of stochastic approximation
methods 80 References for Part II 90 III Applications to adaptation
algorithms (L."
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