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Discrete‐time mixed ℋ︁ 2 /ℋ︁ ∞ nonlinear filtering
Author(s) -
Aliyu M. D. S.,
Boukas E. K.
Publication year - 2010
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1643
Subject(s) - discrete time and continuous time , mathematics , algebraic number , nonlinear system , affine transformation , algebraic riccati equation , filtering problem , matrix (chemical analysis) , filter (signal processing) , algebraic equation , riccati equation , linear system , control theory (sociology) , control (management) , kalman filter , mathematical analysis , pure mathematics , partial differential equation , computer science , extended kalman filter , physics , statistics , materials science , quantum mechanics , artificial intelligence , composite material , computer vision
In this paper, we consider the discrete‐time mixed ℋ 2 /ℋ ∞ filtering problem for affine nonlinear systems. Necessary and sufficient conditions for the solvability of this problem with a finite‐dimensional filter are given in terms of a pair of coupled discrete‐time Hamilton–Jacobi‐Isaac's equations (DHJIE) with some side‐conditions. For linear systems, it is shown that these conditions reduce to a pair of coupled discrete‐time algebraic‐Riccati‐equations (DAREs) or a system of linear matrix inequalities (LMIs) similar to the ones for the control case. Both the finite‐horizon and infinite‐horizon problems are discussed. Moreover, sufficient conditions for approximate solvability of the problem are also derived. These solutions are especially useful for computational purposes, considering the difficulty of solving the coupled DHJIEs. An example is also presented to demonstrate the approach. Copyright © 2010 John Wiley & Sons, Ltd.