Accelerating tube-based model predictive control by constraint removal

Tube-based model predictive control (MPC) is a variant of MPC that is suitable for constrained linear systems subject to additive bounded disturbances. We extend constraint removal, a technique recently introduced to accelerate nominal MPC, to tube-based MPC. Constraint removal detects inactive constraints before actually solving the MPC problem. By removing constraints that are known to be inactive from the optimization problem, the computational time required to solve it can be reduced considerably. We show that the number of constraints to be considered in the optimization problem decreases along any trajectory of the closed-loop system, until only the unconstrained optimization problem remains. The proposed variant of constraint removal is easy to apply. Since it does not depend on details of the optimization algorithm, it can easily be added to existing implementations of tube-based MPC.