Convex Liftings: Theory and Control Applications

Ngocanh A Nguyen (1) , Martin Gulan (2) , Sorin Olaru (3, 4) , Pedro Rodriguez-Ayerbe (4)

1 Institute for Design and Control of Mechatronical Systems
2 STU - Slovak University of Technology in Bratislava
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
4 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 a numerical example and a complexity analysis.

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

Domaines: Automatique / Robotique

Ngocanh A Nguyen, Martin Gulan, Sorin Olaru, Pedro Rodriguez-Ayerbe. Convex Liftings: Theory and Control Applications. IEEE Transactions on Automatic Control, 2017, pp.1. ⟨10.1109/TAC.2017.2737234⟩. ⟨hal-01720262⟩