Simulation, model-reduction, and state estimation of a two-component coagulation process

The issue of state estimation of an aggregation process through (1) using model reduction to obtain a tractable approximation of the governing dynamics and (2) designing a fast moving-horizon estimator for the reduced-order model is addressed. The method of moments is first used to reduce the governing integro-differential equation down to a nonlinear ordinary differential equation. This reduced-order model is then simulated for both batch and continuous processes and the results are shown to agree with constant Number Monte Carlo simulation results of the original model. Next, the states of the reduced order model are estimated in a moving horizon estimation approach. For this purpose, Carleman linearization is first employed and the nonlinear system is represented in a bilinear form. This representation lessens the computation burden of the estimation problem by allowing for analytical solution of the state variables as well as sensitivities with respect to decision variables.