Finite Time Stabilization of Nonlinear Oscillators Subject to dry Friction
Finite Time Stabilization of Nonlinear Oscillators Subject to dry Friction
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DOI：
10.1007/0-387-29195-4_24
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
S. Adly;H. Attouch;A. Cabot
中科院分区：
文献类型：
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作者：
S. Adly;H. Attouch;A. Cabot
给定一个光滑函数f：本文讨论了一个凸函数Φ：<$n→ <$n的微分包含：其中<$Φ表示Φ的次微分.项Φ（Φ）与单边力学中的摩擦概念密切相关。（S）的轨迹被示出为向（S）的稳态解收敛。在附加的假设0 ∈ int <$Φ（0）（干摩擦的情况）下，我们证明了极限在有限时间内达到.这个结果可能在优化中产生有趣的结果。
Given a smooth functionf: 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) 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.