A Lyapunov function for economic MPC without terminal conditions

We consider nonlinear economic model predictive control (MPC) without terminal constraints or costs. We show that under suitable conditions, consisting of strict dissipativity, the turnpike property and appropriate continuity properties, a practical Lyapunov function exists for the MPC closed loop. This Lyapunov function is given by the optimal value function of the optimal control problem with rotated stage costs originating from the dissipativity condition. Alternative sufficient conditions in terms of suitable controllability properties and finite time optimality of the closed loop trajectories during the transient phase are also discussed.