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Robust ℋ︁ ∞ non‐linear estimation
Author(s) -
Shergei M.,
Shaked U.,
De Souza C. E.
Publication year - 1996
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/(sici)1099-1115(199607)10:4/5<395::aid-acs370>3.0.co;2-n
Subject(s) - estimator , bounded function , linear system , mathematical optimization , mathematics , estimation theory , energy (signal processing) , linear model , noise (video) , linear filter , computer science , control theory (sociology) , algorithm , filter (signal processing) , statistics , artificial intelligence , mathematical analysis , control (management) , image (mathematics) , computer vision
This work investigates the problem of ??? ∞ estimation for uncertain continuous time non‐linear systems with non‐linear time‐varying parameter uncertainty. A non‐linear estimator is looked for so that a prescribed bound on the ratio between the energy of the estimation error and the energy of the noise inputs is achieved for any set of parameters in a prescribed bounded region. Conditions for the existence of such an estimator are not easy to find and we therefore formulate an auxiliary estimation problem for a related system which is obtained from the original one by converting the parameter uncertainty into exogenous bounded energy signals. It is shown that an ??? ∞ non‐linear estimator that solves the auxiliary problem, if one exists, guarantees, when applied to the original problem, the required performance for all possible parameters. This approach allows us to solve the robust non‐linear ??? ∞ estimation problem via recently developed ??? ∞ non‐linear filtering techniques. The results are demonstrated by a simple example.