Reducing the computational effort of min-max model predictive control with regional feedback laws

TL;DR

This paper introduces a regional MPC approach for min-max control problems that reduces computational effort by using local affine feedback laws, avoiding the need to solve multiple QPs.

Contribution

It extends regional MPC to min-max problems, significantly decreasing the number of QPs solved and providing guidelines for approach selection based on horizon length.

Findings

Reduces the number of QPs in min-max MPC

Improves computational efficiency significantly

Provides a horizon-based approach selection rule

Abstract

Recently, a regional MPC approach has been proposed that exploits the piecewise affine structure of the optimal solution (without computing the entire explicit solution before). Here, regional refers to the idea of using the affine feedback law that is optimal in a vicinity of the current state of operation, and therefore provides the optimal input signal without requiring to solve a QP. In the present paper, we apply the idea of regional MPC to min-max MPC problems. We show that the new robust approach can significantly reduce the number of QPs to be solved within min-max MPC resulting in a reduced overall computational effort. Moreover, we compare the performance of the new approach to an existing robust regional MPC approach using a numerical example with varying horizon. Finally, we provide a rule for choosing a suitable robust regional MPC approach based on the horizon.