Lifting-based PWA control: A global solution to handle disturbances in the state space partitions

This paper presents a global strategy to address the robustness and fragility of Piecewise Affine (PWA) control, which arises from geometrical perturbations in state-space partitions. Existing methods, which handle perturbations using vertex-based or halfspace-based region representations, are limited to local adjustments of vertices or hyperplanes. In contrast, this paper introduces a novel convex lifting-based region representation that accounts for all subregions of the PWA control perturbation simultaneously. An optimization-based approach is then proposed to enhance the robustness or fragility of the nominal PWA control by refining the lifting-based representation. A numerical example illustrates the effectiveness of the proposed framework.