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Multivalued robust tracking control of fully actuated Lagrange systems: Continuous and discrete–time algorithms

Felix Miranda-Villatoro 1 Bernard Brogliato 2 Fernando Castaños 1 
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 : In this paper the robust trajectory tracking problem of a class of nonlinear systems described by the Euler–Lagrange equations of motion is studied. We start considering a plant under the effects of an unknown external perturbation and also with uncertainties on its parameters. After that a class of passivity-based multivalued control laws is proposed and the well–posedness together with the stability of the closed–loop are established in the continuous–time setting. The discrete–time version of the plant and the controller are studied and well–posedness together with stability results are obtained, using the so-called implicit discretization approach introduced in [1, 2]. Numerical simulations are presented and demonstrate the effectiveness of the proposed discrete-time controller.
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Submitted on : Tuesday, January 12, 2016 - 3:50:08 PM
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Felix Miranda-Villatoro, Bernard Brogliato, Fernando Castaños. Multivalued robust tracking control of fully actuated Lagrange systems: Continuous and discrete–time algorithms. IEEE Transactions on Automatic Control, 2017, 62 (9), pp.4436-4450. ⟨10.1109/TAC.2017.2662804⟩. ⟨hal-01254303⟩

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