  Model predictive control is a powerful framework for enabling optimal control
of constrained systems. However, for systems that are described by
high-dimensional state spaces this framework can be too computationally
demanding for real-time control. Reduced order model predictive control (ROMPC)
frameworks address this issue by leveraging model reduction techniques to
compress the state space model used in the online optimal control problem.
While this can enable real-time control by decreasing the online computational
requirements, these model reductions introduce approximation errors that must
be accounted for to guarantee constraint satisfaction and closed-loop stability
for the controlled high-dimensional system. In this work we propose an offline
methodology for efficiently computing error bounds arising from model
reduction, and show how they can be used to guarantee constraint satisfaction
in a previously proposed ROMPC framework. This work considers linear, discrete,
time-invariant systems that are compressed by Petrov-Galerkin projections, and
considers output-feedback settings where the system is also subject to bounded
disturbances.
