Disturbance observer based fixed time sliding mode control for a class of uncertain second-order nonlinear systems

Zhiqiang Chen; Alexander Yurievich Krasnov; Zhiqiang Chen; Alexander Yurievich Krasnov

doi:10.3934/math.2025309

AIMS Mathematics

2025, Volume 10, Issue 3: 6745-6763. doi: 10.3934/math.2025309

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Disturbance observer based fixed time sliding mode control for a class of uncertain second-order nonlinear systems

Faculty of Control Systems and Robotics, ITMO University, 49 Kronverkskiy ave, St. Petersburg, Leningrad Region, Russia

Received: 11 February 2025 Revised: 13 March 2025 Accepted: 19 March 2025 Published: 26 March 2025
MSC : 93C10

This study investigates the fixed-time control problem for a class of second-order nonlinear systems. Acknowledging that most existing fixed-time sliding mode controllers encounter singularity issues, this paper aims to design a non-singular fixed-time sliding mode controller. Initially, a novel fixed-time sliding mode surface incorporating a sinusoidal function is proposed. Utilizing Lyapunov stability theory, it is rigorously demonstrated that the closed-loop system achieves fixed-time stability under the proposed controller. Furthermore, improvements are introduced to the controller design to mitigate the chattering phenomenon. It is shown that the tracking error converges to a small region around zero within a fixed time. Finally, comparative simulations conducted in MATLAB confirm the effectiveness and superiority of the proposed control algorithm.
- second-order nonlinear system,
- fixed time convergence,
- non-singular sliding mode control,
- chattering
Citation: Zhiqiang Chen, Alexander Yurievich Krasnov. Disturbance observer based fixed time sliding mode control for a class of uncertain second-order nonlinear systems[J]. AIMS Mathematics, 2025, 10(3): 6745-6763. doi: 10.3934/math.2025309

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Abstract

This study investigates the fixed-time control problem for a class of second-order nonlinear systems. Acknowledging that most existing fixed-time sliding mode controllers encounter singularity issues, this paper aims to design a non-singular fixed-time sliding mode controller. Initially, a novel fixed-time sliding mode surface incorporating a sinusoidal function is proposed. Utilizing Lyapunov stability theory, it is rigorously demonstrated that the closed-loop system achieves fixed-time stability under the proposed controller. Furthermore, improvements are introduced to the controller design to mitigate the chattering phenomenon. It is shown that the tracking error converges to a small region around zero within a fixed time. Finally, comparative simulations conducted in MATLAB confirm the effectiveness and superiority of the proposed control algorithm.

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