Piecewise semi-ellipsoidal control invariant sets

TL;DR

This paper introduces a convex programming method for computing control invariant sets using piecewise semi-ellipsoids, offering a less conservative and more flexible alternative to traditional ellipsoids and polyhedra.

Contribution

It proposes a novel convex optimization approach for piecewise semi-ellipsoidal control invariant sets, expanding the tools for complex system control.

Findings

The method effectively computes control invariant sets for complex systems.

Piecewise semi-ellipsoids reduce conservatism compared to traditional ellipsoids.

The approach handles the complexity of polyhedral sets more efficiently.

Abstract

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 paper a convex programming approach for computing control invariant sets of this family.