Abstract
In this chapter we present a mathematical formulation of complementarity dynamical systems with arbitrary dimension and arbitrary relative degree between the complementary slackness variables. The proposed model incorporates the state jumps via high-order distributions through the extension of Moreau’s sweeping process, which is a special type of differential inclusion. The time-discretization of these nonsmooth systems, which is non-trivial, is also presented. Applications of such high-order sweeping processes can be found in dynamic optimization under state constraints and electrical circuits with ideal diodes, where it may be helpful for a better understanding of the closed-loop dynamics induced by some feedback laws.
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Acary, V., Brogliato, B. (2006). Higher Order Moreau’s Sweeping Process. In: Alart, P., Maisonneuve, O., Rockafellar, R.T. (eds) Nonsmooth Mechanics and Analysis. Advances in Mechanics and Mathematics, vol 12. Springer, Boston, MA. https://doi.org/10.1007/0-387-29195-4_22
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DOI: https://doi.org/10.1007/0-387-29195-4_22
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