Prescribed-time trajectory tracking control for a class of nonlinear system

Lichao Feng; Chunlei Zhang; Mahmoud Abdel-Aty; Jinde Cao; Fawaz E. Alsaadi; Lichao Feng; Chunlei Zhang; Mahmoud Abdel-Aty; Jinde Cao; Fawaz E. Alsaadi

doi:10.3934/era.2024305

Electronic Research Archive

2024, Volume 32, Issue 12: 6535-6552. doi: 10.3934/era.2024305

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Prescribed-time trajectory tracking control for a class of nonlinear system

1.
College of Electrical Engineering and College of Science, North China University of Science and Technology, Tangshan 063210, China
2.
Deanship of Graduate Studies and Scientific Research, Ahlia University, Manama 10878, Bahrain
3.
Jadara Research Center, Jadara University. P.O.Box 733, Irbid 21110, Jordan
4.
School of Mathematics, Southeast University, Nanjing 210096, China
5.
Communication Systems and Networks Research Group, Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia

Received: 11 October 2024 Revised: 14 November 2024 Accepted: 20 November 2024 Published: 03 December 2024

Previous works have analyzed finite/fixed-time tracking control for nonlinear systems. In these works, achieving the accurate time convergence of errors must be under the premise of known initial values and careful design of control parameters. Then, how to break through the constraints of initial values and design parameters for this issue is an unsolved problem. Motivated by this, we successfully studied prescribed-time tracking control for single-input single-output nonlinear systems with uncertainties. Specifically, we designed a state feedback controller on $ [0, {T}_{p}) $, based on the backstepping method, to make the tracking error (TE) tend to zero at $ {T}_{p} $, in which $ {T}_{p} $ is the arbitrarily selected prescribed-time. Furthermore, on $ [{T}_{p}, \mathrm{\infty }), $ another controller, similarly to that on $ [0, {T}_{p}) $, was designed to keep TE within a precision after $ {T}_{p} $, while TE may not stay at zero. Therefore, on $ [{T}_{p}, \mathrm{\infty }) $, another new controller, based on sliding mode control, was built to ensure that TE stays at zero after $ {T}_{p}. $
- prescribed-time control,
- backstepping method,
- nonlinear system,
- sliding mode control,
- trajectory tracking
Citation: Lichao Feng, Chunlei Zhang, Mahmoud Abdel-Aty, Jinde Cao, Fawaz E. Alsaadi. Prescribed-time trajectory tracking control for a class of nonlinear system[J]. Electronic Research Archive, 2024, 32(12): 6535-6552. doi: 10.3934/era.2024305

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Abstract

Previous works have analyzed finite/fixed-time tracking control for nonlinear systems. In these works, achieving the accurate time convergence of errors must be under the premise of known initial values and careful design of control parameters. Then, how to break through the constraints of initial values and design parameters for this issue is an unsolved problem. Motivated by this, we successfully studied prescribed-time tracking control for single-input single-output nonlinear systems with uncertainties. Specifically, we designed a state feedback controller on $ [0, {T}_{p}) $, based on the backstepping method, to make the tracking error (TE) tend to zero at $ {T}_{p} $, in which $ {T}_{p} $ is the arbitrarily selected prescribed-time. Furthermore, on $ [{T}_{p}, \mathrm{\infty }), $ another controller, similarly to that on $ [0, {T}_{p}) $, was designed to keep TE within a precision after $ {T}_{p} $, while TE may not stay at zero. Therefore, on $ [{T}_{p}, \mathrm{\infty }) $, another new controller, based on sliding mode control, was built to ensure that TE stays at zero after $ {T}_{p}. $

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