Implicit Euler numerical scheme and chattering-free implementation of sliding mode systems

Vincent Acary 1 Bernard Brogliato 1
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : In this paper it is shown that the implicit Euler time-discretization of some classes of switching systems with sliding modes, yields a very good stabilization of the trajectory and of its derivative on the sliding surface. Therefore the spurious oscillations which are pointed out elsewhere when an explicit method is used, are avoided. Moreover the method (an event-capturing, or time-stepping algorithm) allows for multiple switching surfaces (i.e., a sliding surface of codimension ⩾2). The details of the implementation are given, and numerical examples illustrate the developments. This method may be an alternative method for chattering suppression, keeping the intrinsic discontinuous nature of the dynamics on the sliding surfaces. Links with discrete-time sliding mode controllers are studied.
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Systems and Control Letters, Elsevier, 2010, 59 (5), pp.284-295. 〈10.1016/j.sysconle.2010.03.002〉
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Vincent Acary, Bernard Brogliato. Implicit Euler numerical scheme and chattering-free implementation of sliding mode systems. Systems and Control Letters, Elsevier, 2010, 59 (5), pp.284-295. 〈10.1016/j.sysconle.2010.03.002〉. 〈inria-00423576〉

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