Published: 2015-11-25
ISBN: 978-91-7685-900-1
ISSN: 1650-3686 (print), 1650-3740 (online)
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 manifolds of different dimension. Naturally, this arises in dynamical systems and control applications whenever there are multiple discontinuous control variables. The main aim 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 transversally intersected (n-1)-dimensional switching manifolds in at least p dimensions for any finite (positive) integer p. We explore a new formulation to which we can define unique solutions for such particular behavior in hybrid systems. We illustrate the concepts with examples throughout the paper.
hybrid systems; non-smooth dynamical systems; discontinuity mappings; chattering-free simulation; numerical methods
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