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Journal of Vibration Testing and System Dynamics 10(4) (2026) 313--324 | DOI:10.5890/JVTSD.2026.12.001

Abdul Baseer Satti, Fazal Ur Rehman

Department of Electrical and Computer Systems Engineering, Monash University, Clayton, Australia

Department of Electrical Engineering, Capital University of Science and Technology, Islamabad, Pakistan

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Abstract

This paper explores the control of a class of non-holonomic system using two distinct techniques: adaptive backstepping and stability in finite time through terminal sliding mode control (TSMC), with a particular focus on the Brockett system. An adaptive backstepping-based controller is designed to achieve global uniform asymptotic stability without requiring the conversion of the system model into a chained form, simplifying the implementation. In parallel, TSMC is applied to Brockett's system to achieve finite-time stabilization, providing rapid convergence and robustness against system uncertainties and disturbances. The controllability Lie algebra of Brockett's system contains Lie brackets of depth one, facilitating the application of both methods. Numerical simulations demonstrate the effectiveness of adaptive backstepping for asymptotic stabilization and the capability of TSMC to ensure finite-time convergence. This work underscores the strengths of both techniques in addressing the control challenges of Brockett's system.

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