Control methods for localization of nonlinear waves

Порубов, А. В.; Andrievsky, Boris

doi:10.1098/rsta.2016.0212

Cited by 6 publications

(1 citation statement)

References 21 publications

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“…Recently, the SG algorithms were successfully applied to control of energy in the distributed systems described by a nonlinear PDE (sine-Gordon equation) [38]. Extensions to localization of nonlinear waves problem are presented in [39,40]. The first rigorous results justifying the SG energy control for PDE are obtained in [41].…”

Section: (B) Control Of Wavesmentioning

confidence: 99%

Horizons of cybernetical physics

Fradkov

2017

Phil. Trans. R. Soc. A.

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The subject and main areas of a new research field—cybernetical physics—are discussed. A brief history of cybernetical physics is outlined. The main areas of activity in cybernetical physics are briefly surveyed, such as control of oscillatory and chaotic behaviour, control of resonance and synchronization, control in thermodynamics, control of distributed systems and networks, quantum control. This article is part of the themed issue ‘Horizons of cybernetical physics’.

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Section: (B) Control Of Wavesmentioning

confidence: 99%

Horizons of cybernetical physics

Fradkov

2017

Phil. Trans. R. Soc. A.

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Further progress in control of localized nonlinear waves

Порубов

Antonov

Fradkov

2017

J. Phys.: Conf. Ser.

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Vibrations in engineering systems

Manakova

Mayorov

Сидоров

2019

IOP Conf. Ser.: Mater. Sci. Eng.

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The value of vibration, defined as the oscillatory phenomenon of a solid subjected to the action of force, appeared relatively recently. In fact, mechanical vibration became real only after the industrial revolution. Mechanical oscillatory phenomena, for example, due to working equipment and train movement, began to emerge only by the second half of the eighteenth century. The intensive use of new machines and mechanisms suddenly filled the world, until then, quiet and silent, with new intense noises and vibrations. Different ways of calculating the estimated oscillations of engineering structures, methods of reducing vibrations to the level allowed or their complete isolation, determine the purpose and main problems of the applied theory of mechanical vibrations. In engineering practice, we are almost always interested in predicting the response of a structure or mechanical system to an external effect. For example, we may need to predict the response of a bridge or high-rise building to wind loads, earthquakes, or ground motion. In mechanics and construction, resonant catastrophe describes the destruction of a building or a technical mechanism by induced vibrations at the resonant frequency of a system, which causes its oscillation. Periodic excitation optimally transfers vibration energy to the system and stores it there. Because of this repeated and additional energy input, the system sways more and more until its load limit is exceeded. Frequent reason for these disasters were periodic oscillations of bridges. Periodic fluctuations can be described as a body movement that regularly goes through an equilibrium position. Any oscillatory movement of a mechanical system relative to its equilibrium position is called vibration.

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Control methods for localization of nonlinear waves

Cited by 6 publications

References 21 publications

Horizons of cybernetical physics

Horizons of cybernetical physics

Further progress in control of localized nonlinear waves

Vibrations in engineering systems

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