Model Reduction Near Periodic Orbits of Hybrid Dynamical Systems
Model Reduction Near Periodic Orbits of Hybrid Dynamical Systems
复制标题
混合动力系统近周期轨道的模型简化
DOI：
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发表时间：
2013
影响因子：
6.8
通讯作者：
S. Sastry
中科院分区：
文献类型：
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作者：
Samuel A. Burden;Shai Revzen;S. Sastry
我们证明了在周期轨道附近，一类混合模型可以归结为光滑连续时间动力系统或被光滑连续时间动力系统近似。具体地说，在混合动力系统中，在经历孤立跃迁的指数稳定的周期轨道附近，附近的执行通常以超指数收缩到恒维子系统。在伴随的Poincaré映射的秩亏非退化条件下，无论轨道的稳定性如何，压缩都发生在有限时间内。混合跃迁可以通过允许光滑结构的拓扑商从所得到的子系统中移除，以产生等价的光滑动力系统。我们证明了用于地面运动的高维欠驱动力学模型的降阶，评估了用于有节奏运动和操纵的无差拍控制器的结构稳定性，并推导出混合振荡器稳定域的规范形式。这些应用表明，我们的理论结果对于合成和分析节奏混合行为的反馈控制律是有用的。
We show that, near periodic orbits, a class of hybrid models can be reduced to or approximated by smooth continuous-time dynamical systems. Specifically, near an exponentially stable periodic orbit undergoing isolated transitions in a hybrid dynamical system, nearby executions generically contract super exponentially to a constant-dimensional subsystem. Under a non-degeneracy condition on the rank deficiency of the associated Poincaré map, the contraction occurs in finite time regardless of the stability properties of the orbit. Hybrid transitions may be removed from the resulting subsystem via a topological quotient that admits a smooth structure to yield an equivalent smooth dynamical system. We demonstrate reduction of a high-dimensional underactuated mechanical model for terrestrial locomotion, assess structural stability of deadbeat controllers for rhythmic locomotion and manipulation, and derive a normal form for the stability basin of a hybrid oscillator. These applications illustrate the utility of our theoretical results for synthesis and analysis of feedback control laws for rhythmic hybrid behavior.
影响因子：
2.5
作者：
Ting, LH;Macpherson, JM
通讯作者：
Macpherson, JM