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Convex Liftings: Theory and Control Applications

Abstract : 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.
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Contributor : Ngoc Anh Nguyen <>
Submitted on : Wednesday, July 5, 2017 - 9:55:42 PM
Last modification on : Wednesday, September 16, 2020 - 5:26:23 PM


Convex liftings theory and app...
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  • HAL Id : hal-01326804, version 2


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



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