Sufficient conditions for forward invariance and contractivity in hybrid inclusions using barrier functions
Sufficient conditions for forward invariance and contractivity in hybrid inclusions using barrier functions
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DOI：
10.1016/j.automatica.2020.109328
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发表时间：
2021-02-01
期刊：
影响因子：
6.4
通讯作者：
Sanfelice, Ricardo G.
中科院分区：
文献类型：
--
作者：
Maghenem, Mohamed;Sanfelice, Ricardo G.
研究了混合包含模型下混合系统的集不变性和收缩性。在引入障碍函数的概念后，我们研究了具有非唯一解和过早终止解的混合系统的闭集的不同前向不变性和收缩性概念的充分条件。我们考虑集合的前向（前）不变性，这保证了从集合开始的最大解留在集合中，以及（前）收缩性，这进一步要求从集合的边界开始的解立即（连续或离散）向其内部演化。我们的向前不变性和收缩性的条件是无穷小的，并在建议的障碍函数。实例说明了结果。(C)2020爱思唯尔有限公司保留所有权利。
This paper studies set invariance and contractivity in hybrid systems modeled by hybrid inclusions using barrier functions. After introducing the notion of barrier function, we investigate sufficient conditions to guarantee different forward invariance and contractivity notions of a closed set for hybrid systems with nonuniqueness of solutions and solutions terminating prematurely. We consider forward (pre-)invariance of sets, which guarantees that the maximal solutions starting from the set stay in it, and (pre-)contractivity, which further requires that the solutions starting from the boundary of the set evolve immediately (continuously or discretely) towards its interior. Our conditions for forward invariance and contractivity are infinitesimal and in terms of the proposed barrier functions. Examples illustrate the results. (C) 2020 Elsevier Ltd. All rights reserved.