Robust Simulation for Hybrid Systems Chattering Path Avoidance

Ayman Aljarbouh (1) , Benoît Caillaud (1)

1 HYCOMES - Modélisation hybride & conception par contrats pour les systèmes embarqués multi-physiques

The sliding mode approach is recognized as an efficient tool for treating the chattering behavior in hybrid systems. However, the amplitude of chattering, by its nature, is proportional to magnitude of discontinuous control. A possible scenario is that the solution trajectories may successively enter and exit as well as slide on switching mani-folds of different dimensions. Naturally, this arises in dynamical systems and control applications whenever there are multiple discontinuous control variables. The main contribution of this paper is to provide a robust computational framework for the most general way to extend a flow map on the intersection of p intersected (n−1)-dimensional switching manifolds in at least p dimensions. We explore a new formulation to which we can define unique solutions for such particular behavior in hybrid systems and investigate its efficient computation/simulation. We illustrate the concepts with examples throughout the paper.

Mots clés: Hybrid systems; Discontinuity mappings; Numerical methods; Chattering-free simulation; Non-smooth dynamical sys-tems

Domaines: Modélisation et simulation; Systèmes embarqués; Analyse numérique [cs.NA]; Systèmes et contrôle [cs.SY]; Systèmes dynamiques [math.DS]

Ayman Aljarbouh, Benoît Caillaud. Robust Simulation for Hybrid Systems Chattering Path Avoidance. The 56th Conference on Simulation and Modelling (SIMS 56), Linköping University, Oct 2015, Linköping, Sweden. pp.175-185, ⟨10.3384/ecp15119175⟩. ⟨hal-01247074v2⟩