Abstract and Applied Analysis

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

Vadim Azhmyakov

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2016 (2016), Article ID 2091526, 9 pages.

Dates
Received: 8 April 2016
Accepted: 5 May 2016
First available in Project Euclid: 15 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1465991976

Digital Object Identifier
doi:10.1155/2016/2091526

Mathematical Reviews number (MathSciNet)
MR3510923

Zentralblatt MATH identifier
06929351

Citation

Azhmyakov, Vadim. Consistent Approximations of the Zeno Behaviour in Affine-Type Switched Dynamic Systems. Abstr. Appl. Anal. 2016 (2016), Article ID 2091526, 9 pages. doi:10.1155/2016/2091526. https://projecteuclid.org/euclid.aaa/1465991976


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