Wednesday, 16 January 2002: 4:00 PM

Error growth in uncertain systems

In assessing error growth precise knowledge of the time dependent system being perturbed is generally lacking but statistical properties such as the mean and covariance of the background state can often be estimated. In this work methods of stability analysis are extended to better understand error growth in such uncertain systems. Methods for analyzing uncertain time dependent systems in the limit that the time dependence of the statistical fluctuations of the background state are short compared to the time scale of the associated mean operator and in the case in which the statistical fluctuations of the background state are correlated for intervals long compared to the time scale of the associated mean operator are examined. The physically interesting transitional case of background state fluctuation on time scales comparable to those of the mean state is studied using Markov transition models. An important concept for sure systems is that of the optimal perturbation which is the initial condition producing greatest growth over a chosen interval of time. In uncertain systems a similar result can be obtained: there is a sure initial condition producing the greatest expected error growth for the ensemble.

Supplementary URL: http://www.fas.harvard.edu/~epsas/dynamics/predictability/uncertain1.pdf