Title: Explicit feedback synthesis for nonlinear robust model predictive control driven by quasi-interpolation Show Chinese title

Title: 基于拟插值的非线性鲁棒模型预测控制的显式反馈综合

Abstract: 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. Show Chinese abstract

Abstract: 我们提出了 QuIFS（准插值驱动的反馈综合方法）：一种用于显式非线性鲁棒 minimax 模型预测控制（MPC）问题的离线反馈综合算法，并保证了逼近质量。 该技术基于特定类型的基于网格的准插值方案。 QuIFS 算法与 MPC 行业中常用的常规逼近算法截然不同（特别是，它既不基于多参数规划工具，也不涉及核方法），其出发点的本质体现在以下挑战-回答方法中：给定一个误差容限$\varepsilon>0$，在一次操作中计算出一个可行的反馈策略，该策略对于给定的受约束和有界不确定性的非线性系统，一致地$\varepsilon$接近最优的 MPC 反馈策略。 还建立了在近似反馈策略下的闭环稳定性及递归可行性。 我们提供了一组数值例子来说明我们的结果。