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New Trends in Optimal Filtering and Control for Polynomial and Time-Delay Systems

  • Book
  • © 2008

Overview

Authors:
  1. Michael Basin
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  • Presents the state of the art in the area of Optimal Filtering and Control for Polynomial and Time-Delay Systems

Part of the book series: Lecture Notes in Control and Information Sciences (LNCIS)

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Table of contents (5 chapters)

  1. Front Matter

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  2. Optimal Filtering for Polynomial Systems

    • Michael Basin
    Pages 1-45

  3. Further Results: Optimal Identification and Control Problems

    • Michael Basin
    Pages 47-74

  4. Optimal Filtering Problems for Time-Delay Systems

    • Michael Basin
    Pages 75-130

  5. Optimal Control Problems for Time-Delay Systems

    • Michael Basin
    Pages 131-173

  6. Sliding Mode Applications to Optimal Filtering and Control

    • Michael Basin
    Pages 175-197

  7. Back Matter

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About this book

0. 1 Introduction Although the general optimal solution of the ?ltering problem for nonlinear state and observation equations confused with white Gaussian noises is given by the Kushner equation for the conditional density of an unobserved state with respect to obser- tions (see [48] or [41], Theorem 6. 5, formula (6. 79) or [70], Subsection 5. 10. 5, formula (5. 10. 23)), there are a very few known examples of nonlinear systems where the Ku- ner equation can be reduced to a ?nite-dimensional closed system of ?ltering eq- tions for a certain number of lower conditional moments. The most famous result, the Kalman-Bucy ?lter [42], is related to the case of linear state and observation equations, where only two moments, the estimate itself and its variance, form a closed system of ?ltering equations. However, the optimal nonlinear ?nite-dimensional ?lter can be - tained in some other cases, if, for example, the state vector can take only a ?nite number of admissible states [91] or if the observation equation is linear and the drift term in the 2 2 state equation satis?es the Riccati equation df /dx + f = x (see [15]). The complete classi?cation of the “general situation” cases (this means that there are no special - sumptions on the structure of state and observation equations and the initial conditions), where the optimal nonlinear ?nite-dimensional ?lter exists, is given in [95].

Reviews

From the reviews:

"The book under review provides ways to practically use the filtering model … . This book should be of interest to those for whom filtering and control go beyond the mathematics and who would like to have a sense of the gap that exists in that area between theory and practice. It is also a rich source of specific examples." (A. F. Gualtierotti, Mathematical Reviews, Issue 2009 k)

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