Rigorous numerics for piecewise-smooth systems: A functional analytic approach based on Chebyshev series

In this paper, a rigorous computational method to compute solutions of piecewisesmooth systems using a functional analytic approach based on Chebyshev series is introduced. A general theory, based on the radii polynomial approach, is proposed to compute crossing periodic orbits for continuous and discontinuous (Filippov) piecewise-smooth systems. Explicit analytic estimates to carry the computerassisted proofs are presented. The method is applied to prove existence of crossing periodic orbits in a model nonlinear Filippov system and in the Chua’s circuit system. A general formulation to compute rigorously crossing connecting orbits for piecewise-smooth systems is also introduced. Keywords Rigorous numerics · Piecewise smooth systems · Periodic orbits · Contraction mapping theorem · Chebyshev series · Filippov Mathematics Subject Classification (2010) 34A36 · 65P99 · 65L60 · 46B45 · 37M99

• Type: Journal
• Year: 2016
• Where: JCAM
• Authors: Marcio Gameiro, Jean-Philippe Lessard, Yann Ricaud
• Keywords: Algorithms, JCAM 2016