A novel passivity-based energy-shaping tracking control strategy for networked underactuated Euler-Lagrange systems

Bin Zheng; Runlong Peng; Xuewei Ling; Bin Zheng; Runlong Peng; Xuewei Ling

doi:10.3934/math.2026001

AIMS Mathematics

2026, Volume 11, Issue 1: 1-21. doi: 10.3934/math.2026001

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Research article

A novel passivity-based energy-shaping tracking control strategy for networked underactuated Euler-Lagrange systems

1.
School of Information Engineering, Fujian Business University, Fuzhou 350506, China
2.
Shanghai Institute of Applied Mathematics and Mechanics and Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China
3.
School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China

Received: 26 September 2025 Revised: 15 December 2025 Accepted: 24 December 2025 Published: 04 January 2026
MSC : 34H05, 93A16, 93C10

This paper presents the innovative tracking control approach for networked underactuated Euler-Lagrange systems (NUELSs), which employs the energy-shaping method within the passivity-based control framework. By introducing adaptive control techniques and sliding mode variables, two passivity-based control schemes for NUELSs are developed to enhance the reliability and tracking performance. The proposed controllers achieve closed-loop stability and accurate trajectory tracking by shaping the system's energy and assigning appropriate damping, while maintaining robustness in the presence of communication delays. The rigorous Lyapunov-based analysis is conducted to prove that all internal signals remain bounded and that the tracking errors converge asymptotically to zero. Furthermore, numerical simulations further validate the effectiveness of the presented method.
- energy-shaping method,
- networked underactuated Euler-Lagrange systems (NUELSs),
- passivity-based control,
- sliding mode,
- communication delays
Citation: Bin Zheng, Runlong Peng, Xuewei Ling. A novel passivity-based energy-shaping tracking control strategy for networked underactuated Euler-Lagrange systems[J]. AIMS Mathematics, 2026, 11(1): 1-21. doi: 10.3934/math.2026001

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Abstract

This paper presents the innovative tracking control approach for networked underactuated Euler-Lagrange systems (NUELSs), which employs the energy-shaping method within the passivity-based control framework. By introducing adaptive control techniques and sliding mode variables, two passivity-based control schemes for NUELSs are developed to enhance the reliability and tracking performance. The proposed controllers achieve closed-loop stability and accurate trajectory tracking by shaping the system's energy and assigning appropriate damping, while maintaining robustness in the presence of communication delays. The rigorous Lyapunov-based analysis is conducted to prove that all internal signals remain bounded and that the tracking errors converge asymptotically to zero. Furthermore, numerical simulations further validate the effectiveness of the presented method.

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