  Appropriate time discretization is crucial for real-time applications of
numerical optimal control, such as nonlinear model predictive control. However,
if the discretization error strongly depends on the applied control input,
meeting accuracy and sampling time requirements simultaneously can be
challenging using classical discretization methods. In particular, neither
fixed-grid nor adaptive-grid discretizations may be suitable, when they suffer
from large integration error or exceed the prescribed sampling time,
respectively. In this work, we take a first step at closing this gap by
utilizing probabilistic numerical integrators to approximate the solution of
the initial value problem, as well as the computational uncertainty associated
with it, inside the optimal control problem (OCP). By taking the viewpoint of
probabilistic numerics and propagating the numerical uncertainty in the cost,
the OCP is reformulated such that the optimal input reduces the computational
uncertainty insofar as it is beneficial for the control objective. The proposed
approach is illustrated using a numerical example, and potential benefits and
limitations are discussed.
