Explicit Feedback Synthesis Driven by Quasi-Interpolation for Nonlinear Model Predictive Control

In this article, we present quasi-interpolation-driven feedback synthesis (QuIFS): 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 multiparametric programming tools nor does it involve kernel methods), and the essence of its point of departure is encoded in the following <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">challenge-answer</i> approach: Given an error margin <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon &gt;0$</tex-math></inline-formula>, compute in a single stroke a feasible feedback policy that is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">uniformly</i> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula>-close to the optimal MPC feedback policy for a given nonlinear system subjected to constraints and bounded uncertainties. Closed-loop stability guarantees under the approximate feedback policy are also established. We provide a couple of numerical examples to illustrate our results.