  Despite the success of model predictive control (MPC), its application to
high-dimensional systems, such as flexible structures and coupled
fluid/rigid-body systems, remains a largely open challenge due to excessive
computational complexity. A promising solution approach is to leverage reduced
order models for designing the model predictive controller. In this paper we
present a reduced order MPC scheme that enables setpoint tracking while
robustly guaranteeing constraint satisfaction for linear, discrete,
time-invariant systems. Setpoint tracking is enabled by designing the MPC cost
function to account for the steady-state error between the full and reduced
order models. Robust constraint satisfaction is accomplished by solving
(offline) a set of linear programs to provide bounds on the errors due to
bounded disturbances, state estimation, and model approximation. The approach
is validated on a synthetic system as well as a high-dimensional linear model
of a flexible rod, obtained using finite element methods.
