Abstract:

In studies of perturbation dynamics in physical systems, certain specification of the gov-
erning perturbation dynamical system is generally lacking, either because the perturba-
tion system is imperfectly known or because its specification is intrinsically uncertain, 
while a statistical characterization of the perturbation dynamical system is often avail-
able. In this report exact and asymptotically valid equations are derived for the ensemble 
mean and moment dynamics of uncertain systems. These results are used to extend the 
concept of optimal deterministic perturbation of certain systems to uncertain systems. 
Remarkably, the optimal perturbation problem has a simple solution: In uncertain sys-
tems there is a sure initial condition producing the greatest expected second moment 
perturbation growth.