Hybridization methods for the analysis of nonlinear systems
Hybridization methods for the analysis of nonlinear systems
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DOI：
10.1007/s00236-006-0035-7
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发表时间：
2007-02-01
期刊：
影响因子：
0.6
通讯作者：
Girard, Antoine
中科院分区：
文献类型：
--
作者：
Asarin, Eugene;Dang, Thao;Girard, Antoine
在本文中，我们描述了用于分析非线性系统的混合方法的一些最新结果。我们的混合方法的主要思想是将混合系统方法作为系统近似方法应用。更具体地说，我们将复杂系统的状态空间划分为仅在边界上相交的区域，然后用一个更简单的区域来近似其在每个区域中的动态。然后，所得到的混合系统（我们称之为混合）用于产生原始系统的近似分析结果。我们还证明了混合的重要性质，并提出了两种有效的混合构造方法，可以以良好的收敛速度逼近原始非线性系统。
In this article, we describe some recent results on the hybridization methods for the analysis of nonlinear systems. The main idea of our hybridization approach is to apply the hybrid systems methodology as a systematic approximation method. More concretely, we partition the state space of a complex system into regions that only intersect on their boundaries, and then approximate its dynamics in each region by a simpler one. Then, the resulting hybrid system, which we call a hybridization, is used to yield approximate analysis results for the original system. We also prove important properties of the hybridization, and propose two effective hybridization construction methods, which allow approximating the original nonlinear system with a good convergence rate.