Convex Lifting: Theory and Control Applications

Ngoc Anh Nguyen 1, 2 Martin Gulan 3 Sorin Olaru 4, 1, 2 Pedro Rodriguez-Ayerbe 2
4 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : This paper presents the concept of convex lifting 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 online evaluation effort, which play a key role in implementation of piecewise affine controllers. Finally, these results will be illustrated via numerical examples and a complexity analysis.
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[Research Report] CentraleSupelec. 2016
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  • HAL Id : hal-01326804, version 3

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Ngoc Anh Nguyen, Martin Gulan, Sorin Olaru, Pedro Rodriguez-Ayerbe. Convex Lifting: Theory and Control Applications. [Research Report] CentraleSupelec. 2016. 〈hal-01326804v3〉

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