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

Published online by Cambridge University Press:  16 May 2018

BERNARD BROGLIATO
BERNARD BROGLIATO*
Affiliation:
University Grenoble-Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France email: [email protected]
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Abstract

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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 (existence and uniqueness of solutions) obtained in [1] for the autonomous case, extend to the non-autonomous case when u(·) is smooth and piece-wise analytic, after a suitable state transformation is done. Stability issues are discussed. The complexity of such non-smooth 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.

Keywords

34A6034A3834H1593D0593C30
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Special Issue 5: Theory and applications of nonsmooth dynamical systems , October 2018 , pp. 941 - 968
Copyright
Copyright © Cambridge University Press 2018 

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