Impulsive control of conservative periodic equations and systems: Variational approach

Pavel Drábek; Martina Langerová

doi:10.3934/dcds.2018164

Article Contents

2018, Volume 38, Issue 8: 3789-3802. Doi: 10.3934/dcds.2018164

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Impulsive control of conservative periodic equations and systems: Variational approach

Pavel Drábek^1, , and
Martina Langerová^2,

1.
Department of Mathematics and NTIS, University of West Bohemia, Univerzitní 8, 301 00 Plzeň, Czech Republic
2.
NTIS, University of West Bohemia, Univerzitní 8, 301 00 Plzeň, Czech Republic

* Corresponding author: Pavel Drábek
* Corresponding author: Pavel Drábek

Received: June 30, 2017

Revised: October 31, 2017

Published: May 2018

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Abstract

Using the variational structure of the second order periodic problems we find an optimal impulsive control which forces the conservative system into a periodic motion. In particular, our main results concern the system of charged planar pendulums with external disturbances and neglected friction. Such a system might serve as a model for coupled micromechanical array.

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Mathematics Subject Classification: 34A37, 34C15, 34C25, 49J15.

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Figure 1. A model of 2 coupled charged pendulums.

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Figure 2. A model of $N$ mutually attracted pendulums.

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