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Non-autonomous higher-order Moreau's sweeping process: Well-posedness, stability and Zeno trajectories

Bernard Brogliato 1
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]
Abstract : In this article we study the higher-order Moreau's sweeping process introduced in [1], in the case where an exogenous time-varying function u(·) is present in both the linear dynamics and in the unilateral constraints. First we show that the well-posedness results obtained in [1] for the autonomous case, extend to the non-autonomous case when u(·) is analytic, after a suitable state transformation is done. Stability issues are discussed. The complexity of such nonsmooth non-autonomous dynamical systems is illustrated in a particular case named the higher-order bouncing ball, where trajectories with accumulations of jumps are exhibited. Examples from mechanics and circuits illustrate some of the results. The link with complementarity dynamical systems and with switching differential-algebraic equations is made.
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Submitted on : Monday, November 19, 2018 - 10:47:41 AM
Last modification on : Friday, July 17, 2020 - 11:40:04 AM
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Bernard Brogliato. Non-autonomous higher-order Moreau's sweeping process: Well-posedness, stability and Zeno trajectories. European Journal of Applied Mathematics, Cambridge University Press (CUP), 2018, 29 (5), pp.941-968. ⟨10.1017/S0956792518000256⟩. ⟨hal-01722772v2⟩

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