Off-line supervised learning from data of
robustly-stabilizing nonlinear explicit model predictive controllers
(EMPC) is dealt with in this letter. The learning
procedure relies on the construction of a suitably large set
of specifically chosen sampling points of the state space in
which the values of the optimal EMPC control function have
to be computed. When bounding the magnitude of approximation
errors is important for stability or performance
specifications, regular gridding techniques are not feasible
due to the curse of dimensionality arising from the
structural exponential growth of the number of points with
the state dimension. In this note, we consider non-regular
sampling techniques – namely, i.i.d. sampling with uniform
distribution, low-discrepancy sequences and lattice point
sets – that offer a good covering of the state space without
suffering from an unfeasible growth of the number
of points, while preserving at the same time the method
guarantees in terms of robustness and stability. Some theoretical
properties of the proposed sampling schemes are
briefly discussed, and their successful application is showcased
in a practically-relevant optimal heating problem
involving a 21-dimensional state space that rules out the
use of regular gridding techniques.
