Controllability of a multichannel system

Sergei A. Ivanov; Jun Min Wang

doi:10.1016/j.jde.2017.10.024

Controllability of a multichannel system

Sergei A. Ivanov^*, Jun Min Wang

^*Corresponding author for this work

School of Mathematics and Statistics

RAS - Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider the system consisting of K coupled acoustic channels with the different sound velocities c_j. Channels are interacting at any point via the pressure and its time derivatives. Using the moment approach and the theory of exponential families with vector coefficients we establish two controllability results: the system is exactly controllable if (i) the control u_j in the jth channel acts longer than the double travel time of a wave from the start to the end of the j-th channel; (ii) all controls u_j act more than or equal to the maximal double travel time.

Original language	English
Pages (from-to)	2538-2552
Number of pages	15
Journal	Journal of Differential Equations
Volume	264
Issue number	4
DOIs	https://doi.org/10.1016/j.jde.2017.10.024
Publication status	Published - 15 Feb 2018

Keywords

Controllability
Nonharmonic Fourier series Riesz basis

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10.1016/j.jde.2017.10.024

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abstract = "We consider the system consisting of K coupled acoustic channels with the different sound velocities cj. Channels are interacting at any point via the pressure and its time derivatives. Using the moment approach and the theory of exponential families with vector coefficients we establish two controllability results: the system is exactly controllable if (i) the control uj in the jth channel acts longer than the double travel time of a wave from the start to the end of the j-th channel; (ii) all controls uj act more than or equal to the maximal double travel time.",

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AU - Wang, Jun Min

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AB - We consider the system consisting of K coupled acoustic channels with the different sound velocities cj. Channels are interacting at any point via the pressure and its time derivatives. Using the moment approach and the theory of exponential families with vector coefficients we establish two controllability results: the system is exactly controllable if (i) the control uj in the jth channel acts longer than the double travel time of a wave from the start to the end of the j-th channel; (ii) all controls uj act more than or equal to the maximal double travel time.

KW - Controllability

KW - Nonharmonic Fourier series Riesz basis

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VL - 264

SP - 2538

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 4

ER -

Controllability of a multichannel system

Abstract

Keywords

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