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

N1 - Ivanov, D.; Granichin, O.; Pankov, V.; Volkovich, Z. Design of ℓ1 New Suboptimal Fractional Delays Controller for Discrete Non-Minimum Phase System under Unknown-but-Bounded Disturbance. Mathematics 2022, 10, 69. https://doi.org/10.3390/math10010069

PY - 2021/12/26

Y1 - 2021/12/26

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 - non-minimum phase system

KW - fractional delays

KW - unknown-but-bounded noise

KW - stabilizing controller

KW - non-minimum phase system

KW - fractional delays

KW - unknown-but-bounded noise

KW - stabilizing controller

UR - https://www.mdpi.com/2227-7390/10/1/69

M3 - Article

VL - 10

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 1

M1 - 69

ER -