A Reduced Input/Output Dynamic Optimisation Method for Macroscopic and Microscopic Systems

Abstract

Efficient optimisation algorithms based on model reduction methods are essential for the effective design of large-scale macroscopic, microscopic and multiscale systems. A model reduction based optimization scheme for input/output dynamic systems is presented. It is based on a multiple shooting discretization of the dynamic constraints. The reduced optimization framework is developed by combining an Newton-Picard Method [51], which identifies the (typically) low-dimensional slow dynamics of the (dissipative) model in each time subinterval of the multiple shooting discretization, with reduced Hessian techniques for a second reduction to the low-dimensional subspace of the control parameters. Optimal solutions are then computed in an efficient way using only low-dimensional numerical approximations of gradients and Hessians. We demonstrate the capabilities of this framework by performing dynamic optimization using an explicit tubular reactor transient model and by estimating kinetic parameters of a biochemical system whose dynamics are given by a microscopic Monte Carlo simulator.