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A set-valued nested sliding-mode controller

Felix Miranda-Villatoro 1 Fernando Castaños 1 Bernard Brogliato 2 
2 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann
Abstract : We propose a set-valued controller with a signum multifunction nested inside another one. We prove that the controller is well-posed and achieves robust ultimate boundedness in the presence of mismatched, non-vanishing disturbances. Even more, the selected output can be made arbitrarily small. Also, by applying the implicit Euler scheme introduced by Acary and Brogliato [2010], Acary et al. [2012] for matched disturbances, we derive a selection strategy for the discrete-time implementation of the set-valued control law. The discrete-time scheme diminishes chattering substantially.
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Submitted on : Monday, November 6, 2017 - 10:24:43 AM
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Felix Miranda-Villatoro, Fernando Castaños, Bernard Brogliato. A set-valued nested sliding-mode controller. IFAC 2017 - The 20th World Congress of the International Federation of Automatic Control, Jul 2017, Toulouse, France. pp.2971 - 2976, ⟨10.1016/j.ifacol.2017.08.662⟩. ⟨hal-01629187⟩



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