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A Lyapunov-based design of a modified super-twisting algorithm for the Heisenberg system

Abstract : This paper considers the stabilization controller design for the perturbed Heisenberg system. This objective is achieved by the use of a variable structure with an appropriate sliding variable. A modification of the classical super-twisting algorithm (STA), which consists in combining discontinuous and continuous algorithms, is proposed. Preserving the main advantages of the former approach (i.e. finite time convergence and robustness properties), it can reduce the well-known chattering phenomenon which consists in large oscillations in the neighbourhood of the sliding manifold. The strict Lyapunov function, proposed in Moreno & Osorio [(2008) A Lyapunov approach to second order sliding mode controllers and observers. Proceedings of the IEEE Conference on Decision and Control, New Orleans, USA, pp. 2856–2861], is used to study the settling time and the robustness properties of the proposed controller. A comparative study between the proposed algorithm and other existing algorithms is provided in order to show the advantages especially in terms of steady-state error. Finally, the usefulness of the proposed strategy is illustrated through simulations to solve the stabilization problem for a wheeled mobile robot.
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Contributor : Mylène Delrue Connect in order to contact the contributor
Submitted on : Tuesday, December 7, 2021 - 10:23:22 AM
Last modification on : Wednesday, December 8, 2021 - 3:54:03 AM




Michael Defoort, Mohamed Djemai. A Lyapunov-based design of a modified super-twisting algorithm for the Heisenberg system. IMA Journal of Mathematical Control and Information, Oxford University Press (OUP), 2013, 30 (2), pp.185-204. ⟨10.1093/imamci/dns020⟩. ⟨hal-03468427⟩



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