Forward Invariance of Sets for Hybrid Dynamical Systems (Part I)
Forward Invariance of Sets for Hybrid Dynamical Systems (Part I)
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DOI：
10.1109/tac.2018.2882158
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发表时间：
2018-08
影响因子：
6.8
通讯作者：
Jun Chai;R. Sanfelice
中科院分区：
文献类型：
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作者：
Jun Chai;R. Sanfelice
在本文中，工具，研究前向不变性与鲁棒性的干扰，称为鲁棒前向不变性，提出了混合动力系统建模为混合包含。混合包含的微分和差分包含状态和干扰的约束，其定义只需要四个对象。所提出的鲁棒前向不变性概念允许不同类型的解决方案，这样的系统（有和没有干扰），包括解决方案，具有持久的流动和跳跃，这是芝诺，并停止存在后，有限量的（混合）时间。充分条件集享受这样的属性。这些条件是根据定义混合包含体的对象和要呈现鲁棒前向不变的集合给出的。此外，作为特殊情况，这些条件被利用状态结果的名义前向不变性的混合系统没有干扰。此外，结果提供的条件，使类Lyapunov函数的子级集前向不变的建立。控制逆变器系统的分析作为我们的结果的应用。文中还列举了一些学术实例来说明本文的主要思想。
In this paper, tools to study forward invariance properties with robustness to disturbances, referred to as robust forward invariance, are proposed for hybrid dynamical systems modeled as hybrid inclusions. Hybrid inclusions are given in terms of differential and difference inclusions with state and disturbance constraints, for whose definition only four objects are required. The proposed robust forward invariance notions allow for the diverse type of solutions to such systems (with and without disturbances), including solutions that have persistent flows and jumps, that are Zeno, and that stop to exist after finite amount of (hybrid) time. Sufficient conditions for sets to enjoy such properties are presented. These conditions are given in terms of the objects defining the hybrid inclusions and the set to be rendered robust forward invariant. In addition, as special cases, these conditions are exploited to state results on nominal forward invariance for hybrid systems without disturbances. Furthermore, results that provide conditions to render the sublevel sets of Lyapunov-like functions forward invariant are established. Analysis of a controlled inverter system is presented as an application of our results. Academic examples are given throughout this paper to illustrate the main ideas.