Design of ℓ 1 New Suboptimal Fractional Delays Controller for Discrete Non-Minimum Phase System under Unknown-but-Bounded Disturbance

Dmitrii Ivanov, Oleg Granichin, Vikentii Pankov and Zeev Volkovich
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Dmitrii Ivanov: Department of Information Systems Security, Samara National Research University, 443086 Samara, Russia
Oleg Granichin: Laboratory «Control of Complex Systems», Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, 199178 St. Petersburg, Russia
Vikentii Pankov: Science Research and Educational Center “Mathematical Robotics and Artificial Intelligence”, Faculty of Mathematics and Mechanics, Saint Petersburg State University, 199034 St. Petersburg, Russia
Zeev Volkovich: Software Engineering Department, ORT Braude College, Karmiel 21982, Israel

Mathematics, 2021, vol. 10, issue 1, 1-15

Abstract: ℓ 1 -regularization methodologies have appeared recently in many pattern recognition and image processing tasks frequently connected to ℓ 1 -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: non-minimum phase system; fractional delays; unknown-but-bounded noise; stabilizing controller (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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