Convex Liftings: Theory and Control Applications

Ngoc Anh Nguyen (1) , Martin Gulan (2) , Sorin Olaru (3, 4, 5) , Pedro Rodriguez-Ayerbe (5)

1 JKU - University of Linz - Johannes Kepler Universität Linz
2 STU - Slovak University of Technology in Bratislava
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
4 CentraleSupélec
5 L2S - Laboratoire des signaux et systèmes

This paper presents the so-called convex lifting concept which will be proven to enable significant implementation benefits for the class of piecewise affine controllers. Accordingly, two different algorithms to construct a convex lifting for a given polyhedral/polytopic partition will be presented. These two algorithms rely on either the vertex or the halfspace representation of the related polyhedra. Also, we introduce an algorithm to refine a polyhedral partition, which does not admit a convex lifting, into a convexly liftable one. Furthermore, two different schemes will be put forward to considerably reduce both the memory footprint and the runtime complexity which play a key role in implementation of piecewise affine controllers. Finally, these results will be illustrated via numerical examples and a complexity analysis.

Mots clés: Convex lifting; model predictive control; explicit solutions; parametric programming

Domaines: Sciences de l'ingénieur [physics]

Ngoc Anh Nguyen, Martin Gulan, Sorin Olaru, Pedro Rodriguez-Ayerbe. Convex Liftings: Theory and Control Applications. [Research Report] CentraleSupelec. 2016. ⟨hal-01326804v2⟩