A stability governor for constrained linear–quadratic MPC without terminal constraints

Abstract

This paper introduces a supervisory unit, called the stability governor (SG), that provides improved guarantees of stability for constrained linear systems under Model Predictive Control (MPC) without terminal constraints. At each time step, the SG alters the setpoint command supplied to the MPC problem so that the current state is guaranteed to be inside of the region of attraction for an auxiliary equilibrium point. The proposed strategy is shown to be recursively feasible and asymptotically stabilizing for all initial states sufficiently close to any equilibrium of the system. Thus, asymptotic stability of the target equilibrium can be guaranteed for a large set of initial states even when a short prediction horizon is used. A numerical example demonstrates that the stability governed MPC strategy can recover closed-loop stability in a scenario where a standard MPC implementation without terminal constraints leads to divergent trajectories.