Geometric control of hybrid systems. (February 2023)

• Record Type: Journal Article
• Authors: Legat, Benoît; Jungers, Raphaël M.
• Is Part Of: Nonlinear analysis. Volume 47(2023)
• Publication Date: 2023-02
• Subjects: Controller synthesis -- Set invariance -- LMIs -- Scalable methods; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2022.101289
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: In this paper, we present a geometric approach for computing controlled invariant sets for hybrid control systems. While the problem is well studied in the ellipsoidal case, this family is quite conservative for constrained or switched linear systems. We reformulate the invariance of a set as an inequality for its support function that is valid for any convex set. This produces novel algebraic conditions for the invariance of sets with polynomial or piecewise quadratic support functions.