Reduced Order Model Predictive Control For Setpoint Tracking
For control engineers dealing with high-dimensional systems, this work offers a computationally tractable MPC approach with robust guarantees, though it is incremental over existing reduced order MPC methods.
The paper presents a reduced order MPC scheme for setpoint tracking in high-dimensional linear systems, robustly guaranteeing constraint satisfaction. Validation on a flexible rod model shows computational feasibility.
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.