Design of ℓ1 New Suboptimal Fractional Delays Controller for Discrete Non-Minimum Phase System under Unknown-but-Bounded Disturbance

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...

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Bibliographic Details
Published inMathematics (Basel) Vol. 10; no. 1; p. 69
Main Authors Ivanov, Dmitrii, Granichin, Oleg, Pankov, Vikentii, Volkovich, Zeev
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2022
Subjects
Algorithms
Approximation
Combinatorial analysis
Control algorithms
Control theory
Controllers
Data compression
Difference equations
Food science
fractional delays
Image processing
Mathematical analysis
Noise
Noise (mathematics)
non-minimum phase system
Object recognition
Optimization
Partial differential equations
Pattern recognition
Regularization
Regularization methods
Response time
Rounding
Sampling
Signal processing
stabilizing controller
unknown-but-bounded noise
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10010069