“On the Problem of Identification in Compartment Analysis”
Authors: Erik Aarnæs,Affiliation: University of Oslo
Reference: 1980, Vol 1, No 2, pp. 93-103.
Keywords: Linear compartment system, identification, realization theory, Newton-Raphson method, generalized inverse
Abstract: The present paper discusses how the impulse response of an unknown linear multi-compartment system can be used to identify the system and points out some of the problems associated with a unique identification. A method for system identification has been implemented in a computer program. Simulated data have been used to study the accuracy of the identification from the impulse response.
PDF (1974 Kb) DOI: 10.4173/mic.1980.2.3
References:
[1] ATKINS, G.L. (1969). Multicompartment Models for Biological Systems, Methuen.
[2] BEN-ISRAEL, A. (1966). A Newton-Raphson method for the solution of systems of equations, J. math. Analysis Applic., 15, 243-252.
[3] GILBERT, E.G. (1963). Controllability and observability in multivariable control systems, S.I.A.M. J. Control, 1, 128-151.
[4] GOLUB, G.H., REINSCH, C. (1970). Singular value decomposition and least squares solutions, Num. Math., 14, 403-420.
[5] IMSL-REFERENCE MANUAL (1977). IMSL-library 2, edition 6, IMSL, GNB Building, 7500 Bellaire Boulevard, Houston, Texas 77036, U.S.A.
[6] JACKSON, D.D. (1972). Interpretation of inaccurate, insufficient and inconsistent data, Geophys.. J.R. astr. Soc., 28, 97-109.
[7] JACQUES, J.A. (1972). Compartmental Analysis in Biology and Medicine, Elsevier.
[8] KALMAN, R.E. (1963). Mathematical description of linear dynamical systems, S.I.A.M. J. Control, 1, 152-192.
[9] MONOT, C., MARTIN, J. (1974). Reflections on some algorithms for the solution of the inverse problem (identification or adjustment) for linear compartment models, Mathematical Models in Biology and Medicine. edited by N. T. J. Bailey, Bl. Sendov and R. Tsanev (North-Holland), pp. 49-70.
[10] NORWICH, K.H. (1977). Molecular dynamics in biosystems, The Kinetics of Tracers in Intact Organisms.Pergamon Press, p. 119.
[11] OGATA, K. (1967). State Space Analysis of Control Systems, Prentice-Hall.
[12] PENROSE, R. (1955). A generalized inverse for matrices, Proc. Camb. phil. Soc., 51, 406-413;.1956. On best approximate solution of linear matrix equations. Proc. Camb. phil. Soc. 52, 17-19.
[13] RUBINOW, S.I., WINZER, A. (1971). Compartment analysis: an inverse problem, Math. Biosci., 11, 203-247.
[14] SILVERMAN, L.M. (1971). Realization of linear dynamical systems, IEEE Trans. autom. Control, 16, 554-567 doi:10.1109/TAC.1971.1099821
BibTeX:
@article{MIC-1980-2-3,
title={{On the Problem of Identification in Compartment Analysis}},
author={Aarnæs, Erik},
journal={Modeling, Identification and Control},
volume={1},
number={2},
pages={93--103},
year={1980},
doi={10.4173/mic.1980.2.3},
publisher={Norwegian Society of Automatic Control}
};