A Terminal Set Feasibility Governor for Linear Model Predictive Control

The feasibility governor (FG) is an add-on unit for model predictive controllers (MPC) that increases the closed-loop region of attraction by manipulating the applied reference to ensure the underlying optimal control problem is always feasible. The FG requires an estimate of the feasible set of the optimal control problem that underlies the MPC; obtaining this estimate can be computationally intractable for high-dimensional systems. This article proposes a modified FG that bypasses the need for an explicit estimate, instead relying entirely on the MPC terminal set. The proposed FG formulation is proven to be asymptotically stable, exhibits zero-offset tracking, satisfies constraints, and achieves finite-time convergence of the reference. Numerical comparisons featuring an MPC with a long prediction horizon show that the FG+MPC system can achieve a comparable closed-loop performance to long-horizon MPC at a significantly reduced computational cost by suitably detuning the terminal controller to enlarge the terminal set.