Lyapunov Theory for Zeno Stability

Lamperski A.; Ames A. D.

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Lyapunov Theory for Zeno Stability

机译：利雅普诺夫芝诺稳定性理论

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Zeno behavior is a dynamic phenomenon unique to hybrid systems in which an infinite number of discrete transitions occurs in a finite amount of time. This behavior commonly arises in mechanical systems undergoing impacts and optimal control problems, but its characterization for general hybrid systems is not completely understood. The goal of this paper is to develop a stability theory for Zeno hybrid systems that parallels classical Lyapunov theory; that is, we present Lyapunov-like sufficient conditions for Zeno behavior obtained by mapping solutions of complex hybrid systems to solutions of simpler Zeno hybrid systems defined on the first quadrant of the plane. These conditions are applied to Lagrangian hybrid systems, which model mechanical systems undergoing impacts, yielding simple sufficient conditions for Zeno behavior. Finally, the results are applied to robotic bipedal walking.

机译：芝诺行为是混合系统特有的一种动态现象，在有限的时间内会发生无数个离散过渡。这种现象通常发生在受到冲击和最佳控制问题的机械系统中，但是对于一般混合动力系统的特性却尚未完全了解。本文的目的是开发与经典Lyapunov理论相似的Zeno混合系统的稳定性理论。也就是说，我们提出了通过映射复杂混合系统的解到平面第一象限上定义的简单Zeno混合系统的解而获得的Zeno行为的Lyapunov型充分条件。这些条件适用于拉格朗日混合系统，该系统对遭受冲击的机械系统进行建模，从而为Zeno行为提供简单的充分条件。最后，将结果应用于机器人双足步行。

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来源
《IEEE Transactions on Automatic Control》 |2013年第1期|100-112|共13页
作者
Lamperski A.; Ames A. D.;
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作者单位

Control and Dynamical Systems, California Institute of Technology, Pasadena, andyl@cds.caltech.edu;

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正文语种 eng
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关键词
Asymptotic stability; Differential equations; Lyapunov methods; Mechanical systems; Optimal control; Stability analysis; Vectors; Hybrid systems; Lyapunov method; mechanical systems; stability;

机译：渐近稳定性;微分方程;Lyapunov方法;机械系统;最佳控制;稳定性分析;向量;混合系统;Lyapunov方法;机械系统;稳定性;

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Lyapunov Theory for Zeno Stability

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