Constructive approximations of the Zeno dynamics in affine switched systems: The projection based approach

Vadim Azhmyakov, Moises Bonilla, Stefan Pickl, Luz Adriana Guzman Trujillo

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© 2016 American Automatic Control Council (AACC). This paper deals with a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno dynamics. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real-world processes do not present the corresponding behavior, mathematical models of some interconnected engineering systems may be Zeno due to the corresponding formal abstraction. We propose a useful approximative approach to Zeno dynamics, namely, a projection based characterization of this phenomena. A resulting trajectory associated with the Zeno dynamics can finally be described as a result of a specific dynamic projection procedure applied to the original model. We use here the projected dynamic systems methodology. The obtained formal description provides an effective theoretic basis for a constructive treatment of the Zeno behaviour. We also discuss an application of the proposed technique to the conventional sliding mode control processes.
Original languageAmerican English
Number of pages6
StatePublished - 28 Jul 2016
EventProceedings of the American Control Conference -
Duration: 28 Jul 2016 → …


ConferenceProceedings of the American Control Conference
Period28/07/16 → …

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