2020/06/27 by Benoît Legat, Saša V. Raković, Raphaël M. Jungers · 8 citations
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #Algorithm #Combinatorics #Computation #Computer science #Ellipsoid #Geometry #Invariant (physics) #Mathematical analysis #Mathematics #Optimization and Variational Analysis #Piecewise #Polyhedron #Pure mathematics #Regular polygon #acm:93B05 #acm:93B25 #acm:93B40 #acm:93D15 #acm:93D30 #math.OC #msc:93B05 #msc:93B25 #msc:93B40 #msc:93D15 #msc:93D30
paper · pdf · doi:10.1109/lcsys.2020.3005326
published in IEEE Control Systems Letters 5(3), 755-760 (Institute of Electrical and Electronics Engineers) · 7 pages, 3 figures, to be published in IEEE Control Systems Letters
openalex publication_date 2020/06/27 · arxiv created 2020/07/06 · arxiv updated 2020/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Computing control invariant sets is paramount in many applications. The families of sets commonly used for computations are ellipsoids and polyhedra. However, searching for a control invariant set over the family of ellipsoids is conservative for systems more complex than unconstrained linear time invariant systems. Moreover, even if the control invariant set may be approximated arbitrarily closely by polyhedra, the complexity of the polyhedra may grow rapidly in certain directions. An attractive generalization of these two families are piecewise semi-ellipsoids. We provide in this letter a convex programming approach for computing control invariant sets of this family.