Optimal and suboptimal event-triggering in linear model predictive control

We present two event-triggered MPC laws that do not require to solve a quadratic program (QP) in every time step but only upon certain events. We prove one of the control laws results in exactly the same closed-loop behavior as classical MPC. The second control law requires even fewer QPs per time. It is suboptimal w.r.t. the MPC cost function, but still results in asymptotically stable closed-loop behavior. We illustrate the event-triggered MPC laws with two examples.