Reachability Problems - 12th International Conference, RP 2018, Marseille, France, September 24-26, 2018, Proceedings
Reachability Problems - 12th International Conference, RP 2018, Marseille, France, September 24-26, 2018, Proceedings
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可达性问题 - 第 12 届国际会议，RP 2018，法国马赛，2018 年 9 月 24-26 日，会议记录
DOI：
10.1007/978-3-030-00250-3_1
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Alexandre Dit Sandretto J
中科院分区：
文献类型：
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作者：
Alexandre Dit Sandretto J
常微分方程（ODE）是微分方程的一种一般形式。这种数学格式通常用于表示物理系统的动态行为，例如控制系统和化学过程。线性常微分方程通常可以解析求解，而非线性常微分方程可能需要数值方法来获得近似解。对于非线性常微分方程的有效模拟，如显式和隐式保证Runge-Kutta积分方案，也有各种各样的发展。隐式算法主要是基于仿射算法的区域拓扑计算。它允许计算的可达性的非线性常微分方程的zonotopic集作为其初始值。在本文中，我们提出了一个新的验证方法来解决非线性常微分方程的多面体集作为初始值使用间接实现多面体集计算技术。
Ordinary Differential Equations (ODEs) are a general form of differential equations. This mathematical format is often used to represent the dynamic behavior of physical systems such as control systems and chemical processes. Linear ODEs can usually be solved analytically while nonlinear ODEs may need numerical methods to obtain approximate solutions. There are also various developments for validated simulation of nonlinear ODEs such as explicit and implicit guaranteed Runge-Kutta integration schemes. The implicit ones are mainly based on zonotopic computations using affine arithmetics. It allows to compute the reachability of a nonlinear ODE with a zonotopic set as its initial value. In this paper, we propose a new validated approach to solve nonlinear ODEs with a polytopic set as the initial value using an indirectly implemented polytopic set computation technique.