On notions and sufficient conditions for forward invariance of sets for hybrid dynamical systems
On notions and sufficient conditions for forward invariance of sets for hybrid dynamical systems
复制标题
关于混合动力系统集合前向不变性的概念和充分条件
DOI：
10.1109/cdc.2015.7402652
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
R. Sanfelice
中科院分区：
文献类型：
--
作者：
Jun Chai;R. Sanfelice
研究了混合动力系统的前向不变性问题，该系统由微分包含和差分包含建模，并具有允许流和跳的状态依赖条件。前向不变性的几个概念被认为是定义系统的对象的充分条件。特别是，我们研究了向前不变性的概念，适用于系统的非线性动力学，不是每个解决方案是唯一的，或可能存在任意长的混合时间。这种行为在混合动力系统中非常常见。基于李雅普诺夫的条件也提出了不变集的估计。最后给出了应用和例子来说明结果。特别是，这些结果可应用于弱前向不变集的估计，这是在采用不变性原理研究解的收敛性时感兴趣的不变性性质。
Forward invariance for hybrid dynamical systems modeled by differential and difference inclusions with state-depending conditions enabling flows and jumps is studied. Several notions of forward invariance are considered and sufficient conditions in terms of the objects defining the system are introduced. In particular, we study forward invariance notions that apply to systems with nonlinear dynamics for which not every solution is unique or may exist for arbitrary long hybrid time. Such behavior is very common in hybrid systems. Lyapunov-based conditions are also proposed for the estimation of invariant sets. Applications and examples are given to illustrate the results. In particular, the results are applied to the estimation of weakly forward invariant sets, which is an invariance property of interest when employing invariance principles to study convergence of solutions.