Construction of convex liftings based on halfspace representation

This paper presents a new algorithm to construct convex lifting for a given polyhedral partition whenever it exists. This algorithm exclusively relies on the halfspace representation of the regions in the respective partition. Also, this algorithm is applicable for the general polyhedral partitions of polyhedra, and thus overcomes the limitation on the polytopic partitions of the existing algorithm based on the vertex representation. Finally, the importance of the proposed algorithm is clarified via some numerical examples, in particular in implementation of piecewise affine controllers. Accordingly, the convex lifting concept is shown to be useful to both avoid storing the state-space partition and to facilitate the online evaluation.

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