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

• Michael Basin
• Couverture cartonnée
• 208 Nombre de pages
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This book presents the state-of-the-art in optimal filtering and control for polynomial and time-delay systems.0. 1 Introduction A... Lire la suite
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## Description

This book presents the state-of-the-art in optimal filtering and control for polynomial and time-delay systems.

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].

Résumé
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)

Contenu

Optimal Filtering for Polynomial Systems.- Further Results: Optimal Identification and Control Problems.- Optimal Filtering Problems for Time-Delay Systems.- Optimal Control Problems for Time-Delay Systems.- Sliding Mode Applications to Optimal Filtering and Control.

## Informations sur le produit

 Titre: New Trends in Optimal Filtering and Control for Polynomial and Time-Delay Systems Auteur: Michael Basin Code EAN: 9783540708025 ISBN: 978-3-540-70802-5 Format: Couverture cartonnée Genre: Technique chaleur et énergie nombre de pages: 208 Poids: 365g Taille: H12mm x B235mm x T155mm Année: 2008