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Mixed ℋ︁ 2 /ℋ︁ ∞ nonlinear filtering
Author(s) -
Aliyu M. D. S.,
Boukas E. K.
Publication year - 2008
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.1318
Subject(s) - nonlinear system , affine transformation , mathematics , filter (signal processing) , scheme (mathematics) , riccati equation , horizon , control theory (sociology) , control (management) , mathematical optimization , computer science , mathematical analysis , pure mathematics , partial differential equation , physics , geometry , quantum mechanics , artificial intelligence , computer vision
In this paper, we consider the mixed ℋ 2 /ℋ ∞ filtering problem for affine nonlinear systems. Sufficient conditions for the solvability of this problem with a finite‐dimensional filter are given in terms of a pair of coupled Hamilton–Jacobi–Isaacs equations (HJIEs). For linear systems, it is shown that these conditions reduce to a pair of coupled Riccati equations similar to the ones for the control case. Both the finite‐horizon and the infinite‐horizon problems are discussed. Simulation results are presented to show the usefulness of the scheme, and the results are generalized to include other classes of nonlinear systems. Copyright © 2008 John Wiley & Sons, Ltd.