Finite-time transient control of uncertain nonlinear systems based on prescribed performance and disturbance observer

Yuhong Huo; Wei Xiang; Yuhong Huo; Wei Xiang

doi:10.3934/math.20251112

AIMS Mathematics

2025, Volume 10, Issue 11: 25137-25153. doi: 10.3934/math.20251112

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Finite-time transient control of uncertain nonlinear systems based on prescribed performance and disturbance observer

Yuhong Huo ^1,2,
Wei Xiang ^{2
,
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1.
School of Aeronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2.
School of Finance and Mathematics, Huainan Normal University, Huainan, 232038, China

Received: 31 August 2025 Revised: 07 October 2025 Accepted: 20 October 2025 Published: 03 November 2025
MSC : 93C10, 93C42

For uncertain nonlinear systems with dead-zone input, this paper focuses on designing a disturbance observer-based adaptive fuzzy finite-time prescribed performance controller. To meet practical requirements, a fixed-time disturbance observer is constructed to estimate the system uncertainties. To confine the tracking error within a predefined range, a finite-time performance function is introduced. Subsequently, the constrained problem is transformed into a stability problem via a transformation function. Based on Lyapunov stability theory, the proposed control method can ensure that the closed-loop signals are bounded and the tracking error is restricted within the prescribed range. The simulation results confirm the validity of the proposed approach.
- nonlinear system,
- disturbance observer,
- performance function,
- finite time
Citation: Yuhong Huo, Wei Xiang. Finite-time transient control of uncertain nonlinear systems based on prescribed performance and disturbance observer[J]. AIMS Mathematics, 2025, 10(11): 25137-25153. doi: 10.3934/math.20251112

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Abstract

For uncertain nonlinear systems with dead-zone input, this paper focuses on designing a disturbance observer-based adaptive fuzzy finite-time prescribed performance controller. To meet practical requirements, a fixed-time disturbance observer is constructed to estimate the system uncertainties. To confine the tracking error within a predefined range, a finite-time performance function is introduced. Subsequently, the constrained problem is transformed into a stability problem via a transformation function. Based on Lyapunov stability theory, the proposed control method can ensure that the closed-loop signals are bounded and the tracking error is restricted within the prescribed range. The simulation results confirm the validity of the proposed approach.

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