On inherent limitations in robustness and performance for a class of prescribed-time algorithms

Aldana-López, Rodrigo; Seeber, Richard; Haimovich, Hernan; Gómez-Gutiérrez, David

doi:10.1016/j.automatica.2023.111284

Cited by 11 publications

(1 citation statement)

References 17 publications

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“…In the delay-free case, the mentioned time-dependent controller rejects matched additive disturbances of unknown magnitude, 13 but it is very sensitive with respect to measurement noise. 15,24 The main reason of such sensitivity is the time dependence of the feedback gain which, independently of the stabilization error and the magnitude of the measurement noise, infinitely amplifies the noise as time tends to the prescribed time T. To improve the robustness, a switching rule between time-dependent prescribed-time regulator and a static finite-time (sliding mode) stabilizer has been suggested in Reference 15.…”

Section: Introductionmentioning

confidence: 99%

Fixed‐time stabilization with a prescribed constant settling time by static feedback for delay‐free and input delay systems

Polyakov,

Krstic

2024

Intl J Robust & Nonlinear

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A static nonlinear homogeneous feedback for a fixed‐time stabilization of a linear time‐invariant (LTI) system is designed in such a way that the settling time is assigned exactly to a prescribed constant for all nonzero initial conditions. The constant convergence time is achieved due to a dependence of the feedback gain of the initial state of the system. The robustness of the closed‐loop system with respect to measurement noise and exogenous perturbations is studied using the concept of Input‐to‐State Stability. Both delay‐free and input delay systems are considered. Theoretical results are illustrated by numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Fixed‐time stabilization with a prescribed constant settling time by static feedback for delay‐free and input delay systems

Polyakov,

Krstic

2024

Intl J Robust & Nonlinear

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Predefined‐time tracking control of multiplicative systems

Muñoz‐Vázquez,

Sánchez‐Torres,

Fernández‐Anaya

et al. 2024

Intl J Robust & Nonlinear

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This article describes a control approach for obtaining predefined‐time robust tracking in multiplicative systems despite positive, bounded, and unknown multiplicative disturbances. The proposed approach is distinguished by imposing predefined‐time convergence, a topic previously studied in conventional calculus in the context of multiplicative systems. Multiplicative calculus is recognized as a beneficial tool that complements standard calculus by simplifying the modeling and comprehension of numerous processes. Simulations are carried out to illustrate that the given control strategy enforces convergence before a predefined time instant and, while inducing robustness against system uncertainties. The findings of this article pave the way for further research into predefined‐time synchronization of multiplicative oscillator systems, which would bring promising implications for data encryption and secure communication.

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Global prescribed-time output feedback control of a class of uncertain nonlinear systems by linear time-varying feedback

Zhang,

Zhou,

Duan

2024

Automatica

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On inherent limitations in robustness and performance for a class of prescribed-time algorithms

Cited by 11 publications

References 17 publications

Fixed‐time stabilization with a prescribed constant settling time by static feedback for delay‐free and input delay systems

Fixed‐time stabilization with a prescribed constant settling time by static feedback for delay‐free and input delay systems

Predefined‐time tracking control of multiplicative systems

Global prescribed-time output feedback control of a class of uncertain nonlinear systems by linear time-varying feedback

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