A fast method for obtaining convex combination coefficients

This technical communiqué presents a novel approach for fast computation of convex combination coefficients based on ray shooting. Such a problem arises in the real-time implementation of many set-based control techniques, which require a computationally efficient solution to cope with systems of high dimension or fast dynamics. The proposed method poses no constraints on the polytope structure and requires only a list of vertices and boundary hyperplanes. In test cases involving polytopes of various dimensions and numbers of vertices, the proposed method provided up to seven-fold reductions in the 95% percentile of computation time, compared with a state-of-the-art technique.