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 a numerical example and a complexity analysis.
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Ngocanh Nguyen, Martin Gulan, Sorin Olaru, Pedro Rodriguez-Ayerbe. Convex Liftings: Theory and Control Applications. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, In press, pp.1. ⟨10.1109/TAC.2017.2737234⟩. ⟨hal-01720262⟩

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