On robustness of the speed-gradient sampled-data energy control for the sine–Gordon equation: The simpler the better

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On robustness of the speed-gradient sampled-data energy control for the sine–Gordon equation: The simpler the better. / Andrievsky, Boris ; Orlov, Yury ; Fradkov, Alexander L.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 117, 106901, 02.2023.

Research output: Contribution to journal › Conference article › peer-review

BibTeX

@article{3c6f4337f3af46ba8e697efee51a55de,

title = "On robustness of the speed-gradient sampled-data energy control for the sine–Gordon equation: The simpler the better",

abstract = "The paper studies robustness with respect to time-sampling of the energy regulation for one-dimensional sine–Gordon system. Such a problem is a new to control of invariants for hyperbolic partial differential equations (PDEs). In the absence of analytic results, the problem is studied numerically. The properties of four sampled-data algorithms are computationally studied with respect to three performance criteria. The four speed gradient algorithms are the “proportional”, “relay”, “adaptive-relay” and combined ones, by using state feedback with in-domain actuators. The three performance criteria are limit error, transient time, and threshold of stability for the sampling interval. An unexpected result is that the best performance for all three criteria was exhibited by the simplest, speed-gradient-proportional, algorithm. Simulation results are also presented for other energy tracking controllers to add insight into the parameter choice for improving the closed-loop robustness in the PDE setting over sampled-data algorithms.",

keywords = "Sine–Gordon equation, Energy regulation, speed-gradient, Time-sampling, In-space actuation, Sampled-data nonlinear systems, Speed-gradient",

author = "Boris Andrievsky and Yury Orlov and Fradkov, {Alexander L.}",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2023",

month = feb,

doi = "10.1016/j.cnsns.2022.106901",

language = "English",

volume = "117",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - On robustness of the speed-gradient sampled-data energy control for the sine–Gordon equation: The simpler the better

AU - Andrievsky, Boris

AU - Orlov, Yury

AU - Fradkov, Alexander L.

PY - 2023/2

Y1 - 2023/2

N2 - The paper studies robustness with respect to time-sampling of the energy regulation for one-dimensional sine–Gordon system. Such a problem is a new to control of invariants for hyperbolic partial differential equations (PDEs). In the absence of analytic results, the problem is studied numerically. The properties of four sampled-data algorithms are computationally studied with respect to three performance criteria. The four speed gradient algorithms are the “proportional”, “relay”, “adaptive-relay” and combined ones, by using state feedback with in-domain actuators. The three performance criteria are limit error, transient time, and threshold of stability for the sampling interval. An unexpected result is that the best performance for all three criteria was exhibited by the simplest, speed-gradient-proportional, algorithm. Simulation results are also presented for other energy tracking controllers to add insight into the parameter choice for improving the closed-loop robustness in the PDE setting over sampled-data algorithms.

AB - The paper studies robustness with respect to time-sampling of the energy regulation for one-dimensional sine–Gordon system. Such a problem is a new to control of invariants for hyperbolic partial differential equations (PDEs). In the absence of analytic results, the problem is studied numerically. The properties of four sampled-data algorithms are computationally studied with respect to three performance criteria. The four speed gradient algorithms are the “proportional”, “relay”, “adaptive-relay” and combined ones, by using state feedback with in-domain actuators. The three performance criteria are limit error, transient time, and threshold of stability for the sampling interval. An unexpected result is that the best performance for all three criteria was exhibited by the simplest, speed-gradient-proportional, algorithm. Simulation results are also presented for other energy tracking controllers to add insight into the parameter choice for improving the closed-loop robustness in the PDE setting over sampled-data algorithms.

KW - Sine–Gordon equation

KW - Energy regulation

KW - speed-gradient

KW - Time-sampling

KW - In-space actuation

KW - Sampled-data nonlinear systems

KW - Speed-gradient

UR - http://www.scopus.com/inward/record.url?scp=85140140135&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/0b7ac4dc-9c86-3e49-9bb5-f42d6d0f9235/

U2 - 10.1016/j.cnsns.2022.106901

DO - 10.1016/j.cnsns.2022.106901

M3 - Conference article

VL - 117

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

M1 - 106901

ER -

ID: 99830832