TY - JOUR

T1 - Stabilizing ℓ-semioptimal fractional controller for discrete non-minimum phase system under unknown-but boundeddisturbance

AU - Ivanov, Dmitriy

AU - Granichin, Oleg

AU - Pankov, Vikentii

AU - Granichina, Olga

PY - 2023/9/30

Y1 - 2023/9/30

N2 - 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 disturbance. When considering the ’worst’ case of disturbance, solving this optimization problem has combinatorial complexity. However, by choosing an appropriate sufficiently high sampling rate, it becomes possible to achieve an arbitrarily small level of suboptimality usinga noncombinatorial algorithm. In this article, we propose using fractional delays to achieve a small level of suboptimality without significantly increasing the sampling rate. We approximate fractional delays by minimizing the ℓ1-norm of the objective function. The proposed approximation of the fractional delay allows obtaining zero additional error for many non-integer solutions. Further more, it is shown that with a non-zero approximation error, the resulting controller may have a smaller additional error than the controller obtained using integer optimization. The theoretical results are illustrated by simulation examples with non-minimum-phase plants of the second and third orders.

AB - 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 disturbance. When considering the ’worst’ case of disturbance, solving this optimization problem has combinatorial complexity. However, by choosing an appropriate sufficiently high sampling rate, it becomes possible to achieve an arbitrarily small level of suboptimality usinga noncombinatorial algorithm. In this article, we propose using fractional delays to achieve a small level of suboptimality without significantly increasing the sampling rate. We approximate fractional delays by minimizing the ℓ1-norm of the objective function. The proposed approximation of the fractional delay allows obtaining zero additional error for many non-integer solutions. Further more, it is shown that with a non-zero approximation error, the resulting controller may have a smaller additional error than the controller obtained using integer optimization. The theoretical results are illustrated by simulation examples with non-minimum-phase plants of the second and third orders.

KW - Optimal control

KW - Robust control

KW - Linear systems

KW - Linear systems

KW - Optimal control

KW - Robust control

UR - https://www.mendeley.com/catalogue/05a79084-01ed-3513-9639-cc1fd6e10458/

U2 - 10.35470/2226-4116-2023-12-2-121-128

DO - 10.35470/2226-4116-2023-12-2-121-128

M3 - Article

VL - 12

SP - 121

EP - 128

JO - Cybernetics and Physics

JF - Cybernetics and Physics

SN - 2223-7038

IS - 2

ER -