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An explicit finite difference method for finite‐time observers
Author(s) -
James Matthew R.
Publication year - 1994
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.4590040607
Subject(s) - discretization , classification of discontinuities , robustness (evolution) , nonlinear system , mathematics , convergence (economics) , finite difference , finite element method , rate of convergence , control theory (sociology) , finite set , grid , observer (physics) , finite volume method , computer science , control (management) , mathematical analysis , geometry , engineering , computer network , biochemistry , chemistry , physics , channel (broadcasting) , structural engineering , quantum mechanics , artificial intelligence , mechanics , economics , gene , economic growth
In this paper we present a numerical method for estimating the current state of a nonlinear control system. We use finite differences to discretize a modified version of the finite‐time observer equations in James. The discretized equations are simple and easily programmed. The convergence and accuracy of the scheme is proved, and the scheme enjoys a number of important properties: availability of rate of convergence estimates, good robustness characteristics, and the ability to handle certain types of discontinuities in the observations. The major disadvantage is that the number of grid points required increases exponentially with the number of state dimensions.