Computing the Evolution of Hybrid Systems using Rigorous Function Calculus
Computing the Evolution of Hybrid Systems using Rigorous Function Calculus
复制标题
使用严格函数微积分计算混合系统的演化
DOI：
10.3182/20120606-3-nl-3011.00063
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
T. Villa
中科院分区：
文献类型：
--
作者：
P. Collins;D. Bresolin;Luca Geretti;T. Villa
摘要 混合系统表现出有限自动机、非线性动态系统和微分方程的所有复杂性，并且极难分析。需要严格的数学方法来在计算过程中实现可证明的近似界限。在本文中，我们描述了一种严格的数值微积分，用于处理可用于计算非线性混合系统演化的函数，以及在混合系统可达性分析工具 Ariadne 中的实现。该方法基于用函数表达进化过程中获得的集合，并计算这些函数的近似值，并且允许计算进化集合的高度精确的近似值。给出了水箱中水位控制的示例。
Abstract Hybrid systems exhibit all the complexities of finite automata, nonlinear dynamic systems and differential equations, and are extremely difficult to analyze. A rigorous mathematical approach is needed to achieve provable approximation bounds along the computations. In this paper we describe a rigorous numerical calculus for working with functions that can be used for computing the evolution of nonlinear hybrid systems, and the implementation in the tool Ariadne for reachability analysis of hybrid systems. The method is based around expressing the sets attained during the evolution in terms of functions, and computing approximations to these functions, and allows highly accurate approximations for the evolved sets to be computed. An example of the control of the water level in a tank is presented.