Partially Observable Linear Systems Under Dependent Noises / Edition 1

by Agamirza E. Bashirov

Overview

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 shastic 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.

Product Details

ISBN-13:	9783764369996
Publisher:	Birkhäuser Basel
Publication date:	03/10/2003
Series:	Systems & Control: Foundations & Applications
Edition description:	2003
Pages:	338
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

1 Basic Elements of Functional Analysis.- 1.1 Sets and Functions.- 1.2 Abstract Spaces.- 1.3 Linear Operators.- 1.4 Weak Convergence.- 2 Basic Concepts of Analysis in Abstract Spaces.- 2.1 Continuity.- 2.2 Differentiability.- 2.3 Measurability.- 2.4 Integrability.- 2.5 Integral and Differential Operators.- 3 Evolution Operators.- 3.1 Main Classes of Evolution Operators.- 3.2 Transformations of Evolution Operators.- 3.3 Operator Riccati Equations.- 3.4 Unbounded Perturbation.- 4 Partially Observable Linear Systems.- 4.1 Random Variables and Processes.- 4.2 Shastic Modelling of Real Processes.- 4.3 Shastic Integration in Hilbert Spaces.- 4.4 Partially Observable Linear Systems.- 4.5 Basic Estimation in Hilbert Spaces.- 4.6 Improving the Brownian Motion Model.- 5 Separation Principle.- 5.1 Setting of Control Problem.- 5.2 Separation Principle.- 5.3 Generalization to a Game Problem.- 5.4 Minimizing Sequence.- 5.5 Linear Regulator Problem.- 5.6 Existence of Optimal Control.- 5.7 Concluding Remarks.- 6 ntrol and Estimation under Correlated White Noises.- 6.1 Estimation: Preliminaries.- 6.2 Filtering.- 6.3 Prediction.- 6.4 Smoothing.- 6.5 Shastic Regulator Problem.- 7 Control and Estimation under Colored Noises.- 7.1 Estimation.- 7.2 Shastic Regulator Problem.- 8 Control and Estimation under Wide Band Noises.- 8.1 Estimation.- 8.2 More About the Optimal Filter.- 8.3 Shastic Regulator Problem.- 9 Control and Estimation under Shifted White Noises.- 9.1 Preliminaries.- 9.2 State Noise Delaying Observation Noise: Filtering.- 9.3 State Noise Delaying Observation Noise: Prediction.- 9.4 State Noise Delaying Observation Noise: Smoothing.- 9.5 State Noise Delaying Observation Noise: Shastic Regulator Prob-lem.- 9.6 Concluding Remarks.- 10 Control and Estimation underShifted White Noises (Revised).- 10.1 Preliminaries.- 10.2 Shifted White Noises and Boundary Noises.- 10.3 Convergence of Wide Band Noise Processes.- 10.4 State Noise Delaying Observation Noise.- 10.5 State Noise Anticipating Observation Noise.- 11 Duality.- 11.1 Classical Separation Principle and Duality.- 11.2 Extended Separation Principle and Duality.- 11.3 Innovation Process for Control Actions.- 12 Controllability.- 12.1 Preliminaries.- 12.2 Controllability: Deterministic Systems.- 12.3 Controllability: Shastic Systems.- Comments.- Bibiography.- Index of Notation.

Editorial Reviews

"The book is very well and carefully written. It is an excellent reference on the complete sets of equations for the optimal controls and for the optimal filters under wide band noises and shifted white noises and their possible application to navigation of spacecraft. Independently, it can serve as a useful reference on the part of functional analysis that is needed for problems of infinite-dimensional linear systems theory. The book is written for both applied mathematicians and theoretically oriented engineers as well as for students at a graduate level. The control community will find this reference an important contribution to the modern control and estimation theory literature."

—Mathematical Reviews

"This book deals with key issues in control theory, namely the interaction between optimal control and observation and/or estimation issues…. The book…will be of interest to researchers in optimal control and estimation."

—Zentralblatt Math

From the Publisher