Partially Observable Linear Systems Under Dependent Noises / by Agamirza E. Bashirov
(Systems & Control: Foundation & Applications)
| データ種別 | 電子ブック |
|---|---|
| 出版情報 | Basel : Birkhäuser Basel : Imprint: Birkhäuser , 2003 |
| 本文言語 | 英語 |
| 大きさ | XXVI, 338 p : online resource |
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| 内容注記 | 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 Stochastic Modelling of Real Processes 4.3 Stochastic 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 Stochastic Regulator Problem 7 Control and Estimation under Colored Noises 7.1 Estimation 7.2 Stochastic Regulator Problem 8 Control and Estimation under Wide Band Noises 8.1 Estimation 8.2 More About the Optimal Filter 8.3 Stochastic 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: Stochastic Regulator Prob-lem 9.6 Concluding Remarks 10 Control and Estimation under Shifted 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: Stochastic Systems Comments Bibiography Index of Notation |
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| 一般注記 | 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 |
| 著者標目 | *Bashirov, Agamirza E. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:System theory FREE:Mathematics FREE:Systems Theory, Control |
| 分 類 | DC23:519 |
| 巻冊次 | ISBN:9783034880220 
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| ISBN | 9783034880220 |
| URL | http://dx.doi.org/10.1007/978-3-0348-8022-0 |
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