Design of ℓ1 new suboptimal fractional delays controller for discrete non-minimum phase system under unknown-but-bounded disturbance

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Design of ℓ₁ new suboptimal fractional delays controller for discrete non-minimum phase system under unknown-but-bounded disturbance. / Ivanov, Dmitrii; Granichin, Oleg ; Pankov, Vikentii; Volkovich, Zeev.

In: Mathematics, Vol. 10, No. 1, 69, 01.01.2022.

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

BibTeX

@article{6e015c1920aa4b00b749f70d03f01348,

title = "Design of ℓ1 new suboptimal fractional delays controller for discrete non-minimum phase system under unknown-but-bounded disturbance",

abstract = "ℓ1-regularization methodologies have appeared recently in many pattern recognition and image processing tasks frequently connected to ℓ1-optimization in the control theory. We consider the problem of optimal stabilizing controller synthesis for a discrete non-minimum phase dynamic plant described by a linear difference equation with an additive unknown-but-bounded noise. Under considering the “worst” case of noise, the solving of these optimization problem has a combinatorial complexity. The choosing of an appropriate sufficiently high sampling rate allows to achieve an arbitrarily small level of suboptimality using a noncombinatorial algorithm. In this paper, we suggest to use fractional delays to achieve a small level of suboptimality without increasing the sampling rate so much. We propose an approximation of the fractional lag with a combination of rounding and a first-order fractional lag filter. The suggested approximation of the fractional delay is illustrated via a simulation example with a non-minimum phase second-order plant. The proposed methodology appears to be suitable to be used in various pattern recognition approaches.",

keywords = "Fractional delays, Non-minimum phase system, Stabilizing controller, Unknown-but-bounded noise, CALCULUS, LINEAR PLANT, LQR, non-minimum phase system, stabilizing controller, PERFORMANCE LIMITATIONS, fractional delays, unknown-but-bounded noise, SELECTION",

author = "Dmitrii Ivanov and Oleg Granichin and Vikentii Pankov and Zeev Volkovich",

note = "Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2022",

month = jan,

day = "1",

doi = "10.3390/math10010069",

language = "English",

volume = "10",

journal = "Mathematics",

issn = "2227-7390",

publisher = "MDPI AG",

number = "1",

}

RIS

TY - JOUR

T1 - Design of ℓ1 new suboptimal fractional delays controller for discrete non-minimum phase system under unknown-but-bounded disturbance

AU - Ivanov, Dmitrii

AU - Granichin, Oleg

AU - Pankov, Vikentii

AU - Volkovich, Zeev

PY - 2022/1/1

Y1 - 2022/1/1

N2 - ℓ1-regularization methodologies have appeared recently in many pattern recognition and image processing tasks frequently connected to ℓ1-optimization in the control theory. We consider the problem of optimal stabilizing controller synthesis for a discrete non-minimum phase dynamic plant described by a linear difference equation with an additive unknown-but-bounded noise. Under considering the “worst” case of noise, the solving of these optimization problem has a combinatorial complexity. The choosing of an appropriate sufficiently high sampling rate allows to achieve an arbitrarily small level of suboptimality using a noncombinatorial algorithm. In this paper, we suggest to use fractional delays to achieve a small level of suboptimality without increasing the sampling rate so much. We propose an approximation of the fractional lag with a combination of rounding and a first-order fractional lag filter. The suggested approximation of the fractional delay is illustrated via a simulation example with a non-minimum phase second-order plant. The proposed methodology appears to be suitable to be used in various pattern recognition approaches.

AB - ℓ1-regularization methodologies have appeared recently in many pattern recognition and image processing tasks frequently connected to ℓ1-optimization in the control theory. We consider the problem of optimal stabilizing controller synthesis for a discrete non-minimum phase dynamic plant described by a linear difference equation with an additive unknown-but-bounded noise. Under considering the “worst” case of noise, the solving of these optimization problem has a combinatorial complexity. The choosing of an appropriate sufficiently high sampling rate allows to achieve an arbitrarily small level of suboptimality using a noncombinatorial algorithm. In this paper, we suggest to use fractional delays to achieve a small level of suboptimality without increasing the sampling rate so much. We propose an approximation of the fractional lag with a combination of rounding and a first-order fractional lag filter. The suggested approximation of the fractional delay is illustrated via a simulation example with a non-minimum phase second-order plant. The proposed methodology appears to be suitable to be used in various pattern recognition approaches.

KW - Fractional delays

KW - Non-minimum phase system

KW - Stabilizing controller

KW - Unknown-but-bounded noise

KW - CALCULUS

KW - LINEAR PLANT

KW - LQR

KW - non-minimum phase system

KW - stabilizing controller

KW - PERFORMANCE LIMITATIONS

KW - fractional delays

KW - unknown-but-bounded noise

KW - SELECTION

UR - http://www.scopus.com/inward/record.url?scp=85121850476&partnerID=8YFLogxK

U2 - 10.3390/math10010069

DO - 10.3390/math10010069

M3 - Article

AN - SCOPUS:85121850476

VL - 10

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 1

M1 - 69

ER -

ID: 90973783