Stochastic Contraction in Riemannian Metrics
Stochastic Contraction in Riemannian Metrics
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黎曼度量中的随机收缩
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
J. Slotine
中科院分区：
文献类型：
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作者：
Quang;J. Slotine
随机收缩分析是近年来发展起来的一种研究非线性随机系统全局稳定性的工具，它基于在适当度量下收敛的微分分析。到目前为止，随机收缩的结果和尖锐的相关性能界限已经建立，只有在专门的情况下，状态独立的指标，这限制了它们的适用性。本文扩展随机收缩分析的情况下，一般的时间和状态相关的黎曼度量，在离散时间和连续时间的设置，从而扩展其适用范围更广的非线性随机动力学。
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic contraction results and sharp associated performance bounds have been established only in the specialized context of state-independent metrics, which restricts their applicability. This paper extends stochastic contraction analysis to the case of general time- and state-dependent Riemannian metrics, in both discrete-time and continuous-time settings, thus extending its applicability to a significantly wider range of nonlinear stochastic dynamics.