Online constraint removal: Accelerating MPC with a Lyapunov function

We show how to use a Lyapunov function to accelerate MPC for linear discrete-time systems with linear constraints and quadratic cost. Our method predicts, in the current time step, which constraints will be inactive in the next time step. These constraints can be removed from the online optimization problem of the next time step. The criterion for the detection of inactive constraints is based on the decrease of the Lyapunov function along the trajectory of the controlled system. The criterion is simple, easy to implement in existing MPC algorithms, and its computational cost is small.