Optimisation and Linear Control of Large Scale Nonlinear Systems: A Review and a Suite of Model Reduction-Based Techniques

摘要

The purpose of this paper is twofold: (1) To provide a concise review of methods, recently presented in the literature, which have developed and/or used model reduction technologies for the optimisation and control of large-scale linear and nonlinear systems and (2) to present an overview of the collection of related technologies that have been developed within our group at the University of Manchester concerning the model reduction-based steady-state and dynamic optimisation of large-scale systems, modelled with black-box dynamic and steady state solvers. Furthermore, a new methodology for the linear model predictive control of large-scale non-linear systems will be presented. It relies on adaptive linearisations of the discretised state-space equations using low-order projections of the system's gradients. The tubular reactor has been used as an illustrative example to demonstrate the capabilities of all the above methods due to its high nonlinearity, exhibited through a number of bifurcations at different parameter combinations, and distributed parameter characteristics.