Unconstrained nonlinear MPC: Performance estimates for sampled-data systems with zero order hold

In this paper, model predictive control (MPC) schemes without stabilizing terminal constraints and/or costs are considered for continuous time systems governed by ordinary differential equations. Satisfactory estimates of the required prediction horizon length such that the MPC closed loop is asymptotically stable were recently proposed. However, their applicability is, in general, limited by the fact that the respective proofs require possible discontinuities of the input functions at arbitrary (and a priori unknown) switching times. We present a technique which allows to determine a suitable discretization accuracy such that the obtained performance bound is arbitrarily well recovered for sampled-data systems with zero order hold.