Model reduction and system identification for master equation control systems

摘要

A master equation describes the continuous-time evolution of a probability distribution, and is characterized by a simple bilinear-like structure and an often-high dimension. We develop a model reduction approach in which the number of possible configurations and corresponding dimension is reduced, by removing improbable configurations and grouping similar ones. Error bounds for the reduction are derived based on a minimum and maximum time scale of interest. An analogous linear identification procedure is then presented, which computes the state and output matrices for a predetermined configuration set. These ideas are demonstrated first in a finite-dimensional model inspired by problems in surface evolution, and then in an infinite-dimensional film growth master equation.