Partially Observable Linear Systems Under Dependent Noises

✍ Scribed by Agamirza E. Bashirov (auth.)

• Publisher: Birkhäuser Basel
• Year: 2003
• Tongue: English
• Leaves: 357
• Series: Systems & Control: Foundation & Applications
• Edition: 1
• Category: Library

✦ Synopsis

Noise is a rich concept playing an underlying role in human activity. Consideration of the noise phenomenon in arts and sciences, respectively, makes the distinction between both domains more obvious. Artists create "deliberate noise"'; the masterpieces of literature, music, modern fine art etc. are those where a clear idea, traditionally related to such concepts as love, is presented under a skilful veil of "deliberate noise". On the contrary, sciences fight against noise; a scientific discovery is a law of nature extracted from a noisy medium and refined.
This book discusses the methods of fighting against noise. It can be regarded as a mathematical view of specific engineering problems with known and new methods of control and estimation in noisy media.
The main feature of this book is the investigation of stochastic optimal control and estimation problems with the noise processes acting dependently on the state (or signal) and observation systems. While multiple early and recent findings on the subject have been obtained and challenging problems remain to be solved, this subject has not yet been dealt with systematically nor properly investigated. The discussion is given for infinite dimensional systems, but within the linear quadratic framework for continuous and finite time horizon. In order to make this book self-contained, some background material is provided.
Consequently, the target readers of this book are both applied mathematicians and theoretically oriented engineers who are designing new technology, as well as students of the related branches. The book may also be used as a reference manual in that part of functional analysis that is needed for problems of infinite dimensional linear systems theory.

✦ Table of Contents

Front Matter....Pages i-xxvi
Basic Elements of Functional Analysis....Pages 1-30
Basic Concepts of Analysis in Abstract Spaces....Pages 31-58
Evolution Operators....Pages 59-92
Partially Observable Linear Systems....Pages 93-128
Separation Principle....Pages 129-158
Control and Estimation under Correlated White Noises....Pages 159-182
Control and Estimation under Colored Noises....Pages 183-196
Control and Estimation under Wide Band Noises....Pages 197-226
Control and Estimation under Shifted White Noises....Pages 227-256
Control and Estimation under Shifted White Noises (Revised)....Pages 257-278
Duality....Pages 279-284
Controllability....Pages 285-310
Back Matter....Pages 311-335

✦ Subjects

Systems Theory, Control