Jonas Mair

Jonas Mair, Lukas Schwenkel, Matthias A. Müller et al.

In this paper, we consider undiscouted infinite-horizon optimal control for deterministic systems with an uncountable state and input space. We specifically address the case when the classic value iteration does not converge. For such systems, we use the Ces`aro mean to define the infinite-horizon optimal control problem and the corresponding infinite-horizon value function. Moreover, for this value function, we introduce the Cesàro value iteration and prove its convergence for the special case of systems with periodic optimal operating behavior. For this instance, we also show that the Cesàro value function recovers the undiscounted infinite-horizon optimal cost, if the latter is well-defined.

Jonas Mair, Lukas Schwenkel, Matthias A. Müller et al.

Operation at steady state is often not optimal when optimizing over an economic cost objective. In many cases, periodic operation yields better performance. Therefore, we derive asymptotic stability guarantees of an economic model predictive control scheme with terminal conditions for systems with optimal periodic operation for a more general setup than existing methods can handle. Moreover, we establish a non-averaged closed-loop performance bound by defining the closed-loop cost via a Cesàro summation instead of ordinary summation. Such a non-averaged performance bound provides new insights for systems with periodic optimal operation.