Abstract
When modelling any system using ordinary differential equations, the problem arises of gauging the sensitivity of state predictions to arbitrary functional perturbations to the right-hand sides of the chosen differential equations. Assuming that a suitable Riemannian measure of the distance or gap between any two states (as possible predictions) has been chosen, a scalar functionr(·) of the state is defined which characterizes the insensitivity of a nominal prediction to finite functional perturbations in the differential equations. The limiting behaviour ofr(·) near the nominal prediction defines a second rank symmetric positive definite tensorM, which provides an easily computed and convenient description of the insensitivity of the nominal predictionin each direction to ‘infinitesimal’ functional perturbations in the model. This theory is fully invariant under arbitrary smooth transformations of state variables.
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Communicated by S. K. Mitter
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Martin, D.H. Prediction sensitivity to functional perturbations in modelling with ordinary differential equations. Appl Math Optim 6, 123–137 (1980). https://doi.org/10.1007/BF01442888
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DOI: https://doi.org/10.1007/BF01442888