论文标题
Conley的一类混合系统的基本定理
Conley's fundamental theorem for a class of hybrid systems
论文作者
论文摘要
我们建立了Conley（i）基本定理的版本和（ii）分解定理的一系列混合动力学系统。 （i）的混合版本断言，此类中每个混合系统都存在全球定义的“混合完整的Lyapunov功能”。由机械和控制设置的动机，物理或工程事件会导致系统管理动态的突然变化，我们的结果适用于在机器人文献中广泛研究的大量拉格朗日混合系统（影响）。正式观看，这些结果将Conley和Franks的结果分别用于度量空间上的连续时间和离散时间动力学系统。但是，我们提供了具体的例子，说明了我们对足够条件的陈述如何仅代表更长的项目的早期一步，即建立正式假设可以和不能赋予拓扑表征的极限行为分区，这使Conley的理论使Conley的理论如此有价值。
We establish versions of Conley's (i) fundamental theorem and (ii) decomposition theorem for a broad class of hybrid dynamical systems. The hybrid version of (i) asserts that a globally-defined "hybrid complete Lyapunov function" exists for every hybrid system in this class. Motivated by mechanics and control settings where physical or engineered events cause abrupt changes in a system's governing dynamics, our results apply to a large class of Lagrangian hybrid systems (with impacts) studied extensively in the robotics literature. Viewed formally, these results generalize those of Conley and Franks for continuous-time and discrete-time dynamical systems, respectively, on metric spaces. However, we furnish specific examples illustrating how our statement of sufficient conditions represents merely an early step in the longer project of establishing what formal assumptions can and cannot endow hybrid systems models with the topologically well characterized partitions of limit behavior that make Conley's theory so valuable in those classical settings.
