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The implicit discretization of the super-twisting sliding-mode control algorithm

Bernard Brogliato 1 Andrey Polyakov 2 Denis Efimov 2
1 TRIPOP [2018-2019] - Modélisation, simulation et commande des systèmes dynamiques non lisses [2018-2019]
Inria Grenoble - Rhône-Alpes, LJK [2016-2019] - Laboratoire Jean Kuntzmann [2016-2019]
2 VALSE - Finite-time control and estimation for distributed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : This paper deals with the analysis of the time-discretization of the super-twisting algorithm, with an implicit Euler method. It is shown that the discretized system is well-posed. The existence of a Lyapunov function with convex level sets is proved for the continuoustime closed-loop system. Then the global asymptotic Lyapunov stability of the unperturbed discrete-time closedloop system is proved. The convergence to the origin in a finite number of steps is proved also in the unperturbed case. Numerical simulations demonstrate the superiority of the implicit method with respect to an explicit discretization with significant chattering reduction.
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Submitted on : Tuesday, October 29, 2019 - 8:22:21 AM
Last modification on : Tuesday, September 29, 2020 - 12:24:15 PM
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Bernard Brogliato, Andrey Polyakov, Denis Efimov. The implicit discretization of the super-twisting sliding-mode control algorithm. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, In press, pp.1-8. ⟨10.1109/TAC.2019.2953091⟩. ⟨hal-02336599⟩

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