Explicit feedback synthesis for nonlinear robust model predictive control driven by quasi-interpolation

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.