  Model predictive controllers use dynamics models to solve constrained optimal
control problems. However, computational requirements for real-time control
have limited their use to systems with low-dimensional models. Nevertheless,
high-dimensional models arise in many settings, for example discretization
methods for generating finite-dimensional approximations to partial
differential equations can result in models with thousands to millions of
dimensions. In such cases, reduced order models (ROMs) can significantly reduce
computational requirements, but model approximation error must be considered to
guarantee controller performance. In this work, a reduced order model
predictive control (ROMPC) scheme is proposed to solve robust, output feedback,
constrained optimal control problems for high-dimensional linear systems.
Computational efficiency is obtained by using projection-based ROMs, and
guarantees on robust constraint satisfaction and stability are provided.
Performance of the approach is demonstrated in simulation for several examples,
including an aircraft control problem leveraging an inviscid computational
fluid dynamics model with dimension 998,930.
