Abstract
Given a smooth function f : ℝn → ℝ and a convex function Φ: ℝn → ℝ, we consider the following differential inclusion:
where ∂Φ denotes the subdifferential of Φ. The term ∂Φ(∂Φ\( \dot x \) ) is strongly related with the notion of friction in unilateral mechanics. The trajectories of (S) are shown to converge toward a stationary solution of (S). Under the additional assumption that 0 ∈ int ∂Φ(0) (case of a dry friction), we prove that the limit is achieved in a finite time. This result may have interesting consequences in optimization.
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Adly, S., Attouch, H., Cabot, A. (2006). Finite Time Stabilization of Nonlinear Oscillators Subject to dry Friction. 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_24
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DOI: https://doi.org/10.1007/0-387-29195-4_24
Publisher Name: Springer, Boston, MA
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