Practical prescribed-time prescribed performance control with asymptotic convergence: A vanishing σ-modification approach

Mehdi GOLESTANI; Yongduan SONG; Weizhen LIU; Guangren DUAN; He KONG

doi:10.1016/j.automatica.2026.112902

Practical prescribed-time prescribed performance control with asymptotic convergence: A vanishing σ-modification approach

Mehdi GOLESTANI
, Yongduan SONG^*
, Weizhen LIU
, Guangren DUAN
, He KONG^*

^*Corresponding author for this work

Division of Industrial Data Science

Research output: Journal Publications › Journal Article (refereed) › peer-review

Abstract

In this paper, we present a method capable of ensuring practical prescribed- time control with guaranteed performance for a class of nonlinear systems in the presence of time-varying parametric and dynamic uncertainties, and uncertain control coefficients. Our design consists of two key steps. First, we construct a performance-rate function that freezes at and after a user- specified time T, playing a crucial role in achieving desired precision within prescribed time T and dealing with unmodeled dynamics. Next, based on this function and a σ-modification strategy in which the leakage term starts to vanish at t ≥ T, we develop an adaptive dynamic surface control framework to reduce control complexity, deal with uncertainties, ensure prescribed performance, practical prescribed-time convergence to a specific region, and ultimately achieve asymptotic convergence. The effectiveness of the proposed control method is validated through numerical simulations.

Original language	English
Article number	112902
Number of pages	9
Journal	Automatica
Volume	187
Early online date	13 Mar 2026
DOIs	https://doi.org/10.1016/j.automatica.2026.112902
Publication status	Published - May 2026

Bibliographical note

Publisher Copyright:
© 2026 Elsevier Ltd

Funding

This work was supported by the National Natural Science Foundation of China (NSFC) under Grant 62550003, W2433161, 62403232 as well as the Science Centre Program of NFSC under Grant 62188101. This work was also funded by the Science, Technology, and Innovation Commission of Shenzhen Municipality, China under Grant No. JCYJ20240813094212017, the Shenzhen Science and Technology Program under Grant No. KQTD20221101093557010, the Guangdong Science and Technology Program under Grant No. 2024B1212010002, and Postdoctoral Fellowship Program of CPSF under Grant No. BX20240149. The material in this paper was not presented at any conference.

Keywords

Adaptive control
Dynamic surface control
Prescribed performance
Prescribed-time stability
Unmodeled dynamics

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10.1016/j.automatica.2026.112902

https://linkinghub.elsevier.com/retrieve/pii/S0005109826000865

Cite this

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title = "Practical prescribed-time prescribed performance control with asymptotic convergence: A vanishing σ-modification approach",

abstract = "In this paper, we present a method capable of ensuring practical prescribed- time control with guaranteed performance for a class of nonlinear systems in the presence of time-varying parametric and dynamic uncertainties, and uncertain control coefficients. Our design consists of two key steps. First, we construct a performance-rate function that freezes at and after a user- specified time T, playing a crucial role in achieving desired precision within prescribed time T and dealing with unmodeled dynamics. Next, based on this function and a σ-modification strategy in which the leakage term starts to vanish at t ≥ T, we develop an adaptive dynamic surface control framework to reduce control complexity, deal with uncertainties, ensure prescribed performance, practical prescribed-time convergence to a specific region, and ultimately achieve asymptotic convergence. The effectiveness of the proposed control method is validated through numerical simulations.",

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author = "Mehdi GOLESTANI and Yongduan SONG and Weizhen LIU and Guangren DUAN and He KONG",

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AU - GOLESTANI, Mehdi

AU - SONG, Yongduan

AU - LIU, Weizhen

AU - DUAN, Guangren

AU - KONG, He

PY - 2026/5

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N2 - In this paper, we present a method capable of ensuring practical prescribed- time control with guaranteed performance for a class of nonlinear systems in the presence of time-varying parametric and dynamic uncertainties, and uncertain control coefficients. Our design consists of two key steps. First, we construct a performance-rate function that freezes at and after a user- specified time T, playing a crucial role in achieving desired precision within prescribed time T and dealing with unmodeled dynamics. Next, based on this function and a σ-modification strategy in which the leakage term starts to vanish at t ≥ T, we develop an adaptive dynamic surface control framework to reduce control complexity, deal with uncertainties, ensure prescribed performance, practical prescribed-time convergence to a specific region, and ultimately achieve asymptotic convergence. The effectiveness of the proposed control method is validated through numerical simulations.

AB - In this paper, we present a method capable of ensuring practical prescribed- time control with guaranteed performance for a class of nonlinear systems in the presence of time-varying parametric and dynamic uncertainties, and uncertain control coefficients. Our design consists of two key steps. First, we construct a performance-rate function that freezes at and after a user- specified time T, playing a crucial role in achieving desired precision within prescribed time T and dealing with unmodeled dynamics. Next, based on this function and a σ-modification strategy in which the leakage term starts to vanish at t ≥ T, we develop an adaptive dynamic surface control framework to reduce control complexity, deal with uncertainties, ensure prescribed performance, practical prescribed-time convergence to a specific region, and ultimately achieve asymptotic convergence. The effectiveness of the proposed control method is validated through numerical simulations.

KW - Adaptive control

KW - Dynamic surface control

KW - Prescribed performance

KW - Prescribed-time stability

KW - Unmodeled dynamics

UR - https://www.scopus.com/pages/publications/105034584613

U2 - 10.1016/j.automatica.2026.112902

DO - 10.1016/j.automatica.2026.112902

M3 - Journal Article (refereed)

SN - 0005-1098

VL - 187

JO - Automatica

JF - Automatica

M1 - 112902

ER -

Practical prescribed-time prescribed performance control with asymptotic convergence: A vanishing σ-modification approach

Abstract

Bibliographical note

Funding

Keywords

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