Constraint removal in linear MPC: An improved criterion and complexity analysis

Constraint removal accelerates model predictive control by detecting inactive constraints at the yet unknown optimal solution and removing them from the online optimization problem. We show in this paper that the number of removed constraints can be increased further by generalizing previously used inactivity criteria. The proposed generalization does not depend on information available at previous time steps, and consequently can also be applied at the initial state. In addition, we provide a detailed analysis of the computational complexity of the proposed variant and of existing constraint removal methods, applied to both active-set (AS) and interior-point (IP) solvers. Finally, we compare the different constraint removal variants in numerical experiments to corroborate the complexity analysis carried out, showing the greatest benefits of the proposed variant, especially with IP solvers.