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2‐DOF nonlinear ℋ︁ ∞ certainty‐equivalent filters (CEFs)
Author(s) -
Aliyu M. D. S.
Publication year - 2011
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.993
Subject(s) - control theory (sociology) , nonlinear system , filter (signal processing) , mathematics , impulse response , linear filter , impulse (physics) , class (philosophy) , degrees of freedom (physics and chemistry) , mathematical analysis , computer science , physics , classical mechanics , control (management) , quantum mechanics , artificial intelligence , computer vision
SUMMARY In this paper, a new theory of two‐degrees‐of‐freedom (2 hbox − DOF ) ℋ ∞ filters as counterparts of 2‐DOF controllers is presented. The theory is also extended to n − DOF filters which bore strong resemblance to linear finite‐impulse‐response filters and hence generalizes this class of filters to the nonlinear continuous‐time case. Sufficient conditions for the solvability of the filter gains are derived in terms of new Hamilton–Jacobi–Isaacs equations which do not involve the system states. This is an improvement over earlier results in which the filter gains are functions of the system states. Simulation results are also presented to support the theory. Copyright © 2011 John Wiley & Sons, Ltd.