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2‐DOF discrete‐time nonlinear ℋ︁ ∞ ‐filters
Author(s) -
Aliyu M. D. S.,
Boukas E. K.
Publication year - 2009
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.1482
Subject(s) - control theory (sociology) , nonlinear system , mathematics , filter (signal processing) , linear filter , impulse response , impulse (physics) , class (philosophy) , nonlinear filter , filter design , mathematical analysis , computer science , physics , control (management) , quantum mechanics , artificial intelligence , computer vision
In this paper, a new theory of two‐degrees‐of‐freedom (2‐DOF)‐ℋ ∞ and certainty‐equivalent filters is presented. Exact and approximate solutions to the nonlinear ℋ ∞ filtering problem using this class of filters are derived in terms of discrete‐time Hamilton–Jacobi–Isaacs equations. The expressions for the filter gains are determined as functions of the filter state and the system's output in contrast to earlier results. Hence, it is shown that coupled with the additional degree‐of‐freedom, these filters are a substantial improvement over the earlier 1‐DOF case. The theory presented is also generalized to n ‐DOF filters, which bore strong connections to linear infinite‐impulse response filters and hence are generalizations of this class of filters to the nonlinear setting. Simulation results are also given to show the usefulness of the new approach. Copyright © 2009 John Wiley & Sons, Ltd.