Adaptive fixed-time stabilization for a class of nonlinear uncertain systems

Yan Zhao; Jianli Yao; Jie Tian; Jiangbo Yu; Yan Zhao; Jianli Yao; Jie Tian; Jiangbo Yu

doi:10.3934/mbe.2023359

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 5: 8241-8260. doi: 10.3934/mbe.2023359

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Research article Special Issues

Adaptive fixed-time stabilization for a class of nonlinear uncertain systems

School of Science, Shandong Jianzhu University, Jinan 250101, China

Received: 07 December 2022 Revised: 07 February 2023 Accepted: 12 February 2023 Published: 28 February 2023

Finite-time stability (FTS) has attained great interest in nonlinear control systems in recent two decades. Fixed-time stability (FxTS) is an improved version of FTS in consideration of its settling time independent of the initial values. In this article, the adaptive fixed-time stabilization issue is studied for a kind of nonlinear systems with nonlinear parametric uncertainties and uncertain control coefficients. Using the adaptive estimate and the adding one power integrator (AOPI) design tool, we propose a two-phase control strategy, which makes that the system states tend to the origin in fixed-time, and other signals are bounded on $ [0, +\infty) $. We prove the main results by means of the recently developed fixed-time Lyapunov stability theory. Finally, we apply the proposed adaptive fixed-time stabilizing control strategy into the pendulum system, and the simulation results verify the efficacy of the presented method.
- finite-time control,
- adaptive control,
- fixed-time stabilization,
- parametric uncertainty
Citation: Yan Zhao, Jianli Yao, Jie Tian, Jiangbo Yu. Adaptive fixed-time stabilization for a class of nonlinear uncertain systems[J]. Mathematical Biosciences and Engineering, 2023, 20(5): 8241-8260. doi: 10.3934/mbe.2023359

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Abstract

Finite-time stability (FTS) has attained great interest in nonlinear control systems in recent two decades. Fixed-time stability (FxTS) is an improved version of FTS in consideration of its settling time independent of the initial values. In this article, the adaptive fixed-time stabilization issue is studied for a kind of nonlinear systems with nonlinear parametric uncertainties and uncertain control coefficients. Using the adaptive estimate and the adding one power integrator (AOPI) design tool, we propose a two-phase control strategy, which makes that the system states tend to the origin in fixed-time, and other signals are bounded on $ [0, +\infty) $. We prove the main results by means of the recently developed fixed-time Lyapunov stability theory. Finally, we apply the proposed adaptive fixed-time stabilizing control strategy into the pendulum system, and the simulation results verify the efficacy of the presented method.

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