Propagation of uncertain inputs through networks of nonlinear components

Physics based models are often converted to monolithic systems of uncertain nonlinear differential/algebraic equations. Graph decomposition methods can be used to decompose such system into subsystems evolving on different time scales. This time scale separation can be exploited to increase computational efficiency when propagating input uncertainty in a subsystem-by-subsystem manner. In this paper, the propagation of uncertain inputs through series, parallel and feedback interconnections of dynamical systems with simple asymptotic behavior is studied by employing discrete density mapping (analogous to the input-output Perron-Frobenius operator). A simple example is used to illustrate the method.