Computation of periodic solutions in maximal monotone dynamical systems with guaranteed consistency. (May 2017)

• Record Type: Journal Article
• Authors: Heemels, W.P.M.H.; Sessa, V.; Vasca, F.; Camlibel, M.K.
• Is Part Of: Nonlinear analysis. Volume 24(2017)
• Page Start: 100
• Page End: 114
• Publication Date: 2017-05
• Subjects: Hybrid systems -- Set-valued dynamical systems -- Computational methods -- Periodic solutions -- Stability of nonlinear systems -- Maximal monotonicity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2016.10.006
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: In this paper, we study a class of set-valued dynamical systems that satisfy maximal monotonicity properties. This class includes linear relay systems, linear complementarity systems, and linear mechanical systems with dry friction under some conditions. We discuss two numerical schemes based on time-stepping methods for the computation of the periodic solutions when these systems are periodically excited. We provide formal mathematical justifications for the numerical schemes in the sense of consistency, which means that the continuous-time interpolations of the numerical solutions converge to the continuous-time periodic solution when the discretization step vanishes. The two time-stepping methods are applied for the computation of the periodic solution exhibited by a power electronic converter and the corresponding methods are compared in terms of approximation accuracy and computation time.