  We present QuIFS (Quasi-Interpolation driven Feedback Synthesis): an offline
feedback synthesis algorithm for explicit nonlinear robust minmax model
predictive control (MPC) problems with guaranteed quality of approximation. The
underlying technique is driven by a particular type of grid-based
quasi-interpolation scheme. The QuIFS algorithm departs drastically from
conventional approximation algorithms that are employed in the MPC industry (in
particular, it is neither based on multi-parametric programming tools and nor
does it involve kernel methods), and the essence of its point of departure is
encoded in the following challenge-answer approach: Given an error margin
$\varepsilon>0$, compute in a single stroke a feasible feedback policy that is
uniformly $\varepsilon$-close to the optimal MPC feedback policy for a given
nonlinear system subjected to constraints and bounded uncertainties.
Closed-loop stability and recursive feasibility under the approximate feedback
policy are also established. We provide a library of numerical examples to
illustrate our results.
