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Estimation of time- and state-dependent delays and other parameters in functional differential equationsA parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.
Document ID
19900056773
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Murphy, K. A. (North Carolina, University Chapel Hill, United States)
Date Acquired
August 14, 2013
Publication Date
August 1, 1990
Publication Information
Publication: SIAM Journal on Applied Mathematics
Volume: 50
ISSN: 0036-1399
Subject Category
NUMERICAL ANALYSIS
Funding Number(s)
CONTRACT_GRANT: NAS1-17070
CONTRACT_GRANT: AF-AFOSR-86-0256
Distribution Limits
Public
Copyright
Other