Model predictive controllers leverage system 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 many systems naturally produce high-dimensional models,
such as those modeled by partial differential equations that when discretized
can result in models with thousands to millions of dimensions. In such cases
the use of 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 leveraging ROMs obtained via projection-based
techniques, 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.Comment: This work has been submitted to the IEEE Transactions on Automatic
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