In this article we introduce a solution method for a special class of nonlinear initial-value problems using set-based propagation techniques. The novelty of the approach is that we employ a particular embedding (Carleman linearization) to leverage recent advances of high-dimensional reachability solvers for linear ordinary differential equations based on the support function. Using a global error bound for the Carleman linearization abstraction, we are able to describe the full set of behaviors of the system for sets of initial conditions and in dense time.

翻译：在本篇文章中,我们引入了使用基于设定传播技术的非线性初始值特殊类别问题的解决办法。 这种方法的新颖之处在于我们使用一种特定的嵌入式( Carleman 线性化) 来利用高维可达性解析器的最新进展, 用于基于支持功能的线性普通差分方程。 使用卡莱曼线性抽象学的全球错误, 我们可以描述系统在一系列初始条件和密集时间的全套行为。