论文标题
差分夹杂物的高阶方法
Higher Order Method for Differential Inclusions
论文作者
论文摘要
不确定性在建模动态系统中是不可避免的，并且可以通过差分包含在数学上表示。过去，我们提出了一种算法来计算差异夹杂物的经过验证的解决方案。在这里，我们提供了对算法的几种理论改进，包括扩展到不确定输入的分段常数和正弦近似值，仿射近似边界的更新以及分析误差的广义公式。提出的方法能够相对于当前的最新技术实现高阶收敛。我们在Ariadne（用于验证连续和混合系统的库）中实施了方法。出于评估目的，我们从文献中介绍了十个系统，具有不同程度的非线性，变量数量和不确定的输入。与非线性系统中不确定性的两种最先进的方法相比，结果与此相比。
Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide several theoretical improvements to the algorithm, including its extension to piecewise constant and sinusoidal approximations of uncertain inputs, updates on the affine approximation bounds and a generalized formula for the analytical error. The approach proposed is able to achieve higher order convergence with respect to the current state-of-the-art. We implemented the methodology in Ariadne, a library for the verification of continuous and hybrid systems. For evaluation purposes, we introduce ten systems from the literature, with varying degrees of nonlinearity, number of variables and uncertain inputs. The results are hereby compared with two state-of-the-art approaches to time-varying uncertainties in nonlinear systems.
