Prescribed-time non-overshooting tracking control for nonlinear systems via a time-scale transformation approach*

Mengnan Hao, Ning Xu and Ning Zhao

International Journal of Systems Science, 2026, vol. 57, issue 3, 804-815

Abstract: This paper delves into addressing the issue of achieving non-overshooting tracking control within a prescribed time for a class of nonlinear systems. By employing a blow-up function and a time-scale transformation approach, the tracking error system is converted from the original time domain into a scaled system within the transformed time framework. Subsequently, a switching controller is then designed to ensure prescribed-time stability for the original tracking error system, which is achieved by applying a backstepping technique to analyze the global asymptotic stability of the scaled system. Additionally, conditions on the initial states of the tracking error system are provided to ensure the non-overshooting performance of nonlinear systems. Recommendations for selecting controller gains are also derived to guarantee non-overshooting prescribed-time stability under arbitrary initial conditions. Finally, the effectiveness of the proposed method is demonstrated through its application to a wheeled mobile robot system.

Date: 2026
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DOI: 10.1080/00207721.2025.2514587

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