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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 considerable 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 representations 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 significantly 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.
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https://hal-centralesupelec.archives-ouvertes.fr/hal-01326804
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Submitted on : Sunday, June 5, 2016 - 11:36:34 PM
Last modification on : Friday, May 28, 2021 - 5:08:01 PM

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  • HAL Id : hal-01326804, version 1

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Ngoc Anh Nguyen, Martin Gulan, Sorin Olaru, Pedro Rodriguez-Ayerbe. Convex Liftings: Theory and Control Applications. [Research Report] CentraleSupelec. 2016. ⟨hal-01326804v1⟩

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