Summary We consider economic model predictive control (MPC) without terminal conditions for time‐varying optimal control problems. Under appropriate conditions, we prove that MPC yields initial pieces of approximately infinite horizon optimal trajectories and that the optimal infinite horizon trajectory is practically asymptotically stable. The results are illustrated by numerical examples motivated by energy‐efficient heating and cooling of a building.

In this paper we study closed loop performance estimates for economic model predictive control (MPC) of timevarying systems. In order to consider general cost functionals we use the concept of overtaking optimality. Under turnpike and continuity assumptions we show that the cost of the MPC closed loop approximates the cost of an infinite horizon optimal trajectory. The theoretical results are illustrated by a numerical example.

We consider the turnpike property for infinite horizon undiscounted optimal control problems in discrete time and with time-varying data. We show that, under suitable conditions, a time varying strict dissipativity notion implies the turnpike property and a continuity property of the optimal value function. We also discuss the relation of strict dissipativity to necessary optimality conditions and illustrate our results by an example.

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