  For nonlinear (control) systems, extended dynamic mode decomposition (EDMD)
is a popular method to obtain data-driven surrogate models. Its theoretical
foundation is the Koopman framework, in which one propagates observable
functions of the state to obtain a linear representation in an
infinite-dimensional space. In this work, we prove practical asymptotic
stability of a (controlled) equilibrium for EDMD-based model predictive
control, in which the optimization step is conducted using the data-based
surrogate model. To this end, we derive novel bounds on the estimation error
that are proportional to the norm of state and control. This enables us to show
that, if the underlying system is cost controllable, this stabilizablility
property is preserved. We conduct numerical simulations illustrating the proven
practical asymptotic stability.
