Efficient Reachability Bounds for Discrete-Time Nonlinear Systems by Extending the Continuous-Time Theory of Differential Inequalities
Efficient Reachability Bounds for Discrete-Time Nonlinear Systems by Extending the Continuous-Time Theory of Differential Inequalities
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通过扩展微分不等式的连续时间理论实现离散时间非线性系统的有效可达界
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Joseph K. Scott
中科院分区：
文献类型：
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作者：
Xuejiao Yang;Joseph K. Scott
通过扩展基于微分不等式的有效连续时间方法，提出了一种计算离散时间非线性系统可达集紧区间闭包的新方法。DI的最新进展为几个具有挑战性的测试用例提供了非常锋利的外壳，成本很低。然而，这些方法依赖于连续时间系统的关键性质，而不是扩展到离散时间。然而，我们证明了DI方法的离散时间模拟确实为通过连续时间模型的正向欧拉离散化而获得的一类重要系统提供了有效的可达集合封闭，只要步长低于一个容易计算的界。数值实验表明，这一界限是合理的，离散时间DI在速度和精度方面都比其他算法有明显的优势。
This paper presents a new approach for computing tight interval enclosures of the reachable sets of discrete-time nonlinear systems by extending effective continuous-time methods based on differential inequalities (DI). Recent advances in DI have furnished very sharp enclosures at low cost for several challenging test cases. However, these methods rely on key properties of continuous-time systems that do not extend to discrete-time. Nevertheless, we show that discrete-time analogues of DI methods do provide valid reachable set enclosures for the important class of systems obtained by forward Euler discretization of continuous-time models, provided that the step size is below an easily computable bound. Numerical experiments show that this bound is reasonable, and that discrete-time DI offers significant advantages over alternative algorithms in terms of both speed and accuracy.