Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systems

Abstract

Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of the so-called local quadratic support is proved. The results concerning strong convexity are used to derive sufficient conditions for attainable sets of continuous-time nonlinear systems to be strongly convex. An application of these conditions is a novel method to over-approximate attainable sets when strong convexity is present.

20 pages, 3 figures

References in corpus (5)

• Generalized power method for sparse principal component analysis
• NP-hardness of Deciding Convexity of Quartic Polynomials and Related Problems
• Computing abstractions of nonlinear systems
• Convexity of reachable sets of nonlinear ordinary differential equations
• Local characterization of strongly convex sets

Cited by in corpus (1)

• Feedback Refinement Relations for the Synthesis of Symbolic Controllers