Piecewise Semi-Ellipsoidal Control Invariant Sets

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.

Automated summary

Computing control invariant sets is crucial in many applications, with ellipsoids and polyhedra being commonly used families for computations. However, searching for a control invariant set over the family of ellipsoids may be conservative for more complex systems, while polyhedra may grow rapidly in complexity in certain directions. A promising generalization of these families is piecewise semi-ellipsoids, for which we provide a convex programming approach in this letter.