Schatten-p radius: Optimality criterion and optimization for basic ellipsotopes with application to zonotopes and ellipsoids

Abstract

Optimizing a parameterized zonotope or ellipsoid is a common task in robust state estimation, fault diagnosis and reachability analysis. Recent studies have unified ellipsoids and zonotopes into basic ellipsotopes, which support precise representation for more nonlinear boundaries and constraints in practical applications. However, there are currently no available optimality criteria and optimization techniques for general basic ellipsotopes. In this paper, we introduce a novel optimality criterion called Schatten-p radius for basic ellipsotopes. Based on this criterion, we develop a set of methods to minimize the Schatten-p radius under convex constraints for arbitrary $0<$ p $<\infty$, which also implies new available tools for minimizing zonotopes and ellipsoids. The effectiveness of the Schatten-p radius optimization is demonstrated on several numerical examples.