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Consistent Approximations of the Zeno Behaviour in Affine‐Type Switched Dynamic Systems

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  • Vadim Azhmyakov

Abstract

This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. 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 behaviour, mathematical models of many engineering systems may be Zeno due to the used formal abstraction. We propose two useful approximative approaches to the Zeno dynamics, namely, an analytic technique and a variational description of this phenomenon. A generic trajectory associated with the Zeno dynamics can finally be characterized as a result of a specific projection or/and an optimization procedure applied to the original dynamic model. The obtained analytic and variational techniques provide an effective methodology for constructive approximations of the general Zeno‐type behaviour. We also discuss shortly some possible applications of the proposed approximation schemes.

Suggested Citation

  • Vadim Azhmyakov, 2016. "Consistent Approximations of the Zeno Behaviour in Affine‐Type Switched Dynamic Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnlaaa:v:2016:y:2016:i:1:n:2091526
    DOI: 10.1155/2016/2091526
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    1. Vadim Azhmyakov & Marco Angulo, 2011. "Applications of the strong approximability property to a class of affine switched systems and to relaxed differential equations with affine structure," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(11), pages 1899-1907.
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