Accurate Uncertainty Propagation for Discrete-Time Nonlinear Systems Using Differential Inequalities With Model Redundancy
Accurate Uncertainty Propagation for Discrete-Time Nonlinear Systems Using Differential Inequalities With Model Redundancy
复制标题
使用微分不等式和模型冗余的离散时间非线性系统的精确不确定性传播
DOI：
10.1109/tac.2020.2968241
复制
发表时间：
2020
影响因子：
6.8
通讯作者：
Xuejiao Yang
中科院分区：
文献类型：
--
作者：
Xuejiao Yang
本文提出了一种新的计算离散时间非线性系统可达集的紧区间包络的方法。这些方法的动机是基于微分不等式（DI）的连续时间系统的有效方法。现代DI方法，特别是那些使用基于冗余模型方程的细化技术，已经证明了非常尖锐的外壳在几个具有挑战性的测试用例的低成本。然而，它们依赖于连续时间系统的关键特性，而这些特性在离散时间中通常不成立。尽管如此，我们表明，这些方法的离散时间模拟提供了有效的外壳系统满足一定的单调性条件。我们表明，这些条件总是满足系统的连续时间模型的步长低于一个可计算的上限向前欧拉离散化。新的细化算法，提出了利用冗余模型方程的离散时间设置。所得到的离散时间DI方法相比，现有的算法使用几个案例研究。
This article presents new methods for computing tight interval enclosures of the reachable sets of discrete-time nonlinear systems subject to bounded uncertainties. These methods are motivated by effective methods for continuous-time systems based on differential inequalities (DI). Modern DI methods, particularly those using refinement techniques based on redundant model equations, have demonstrated very sharp enclosures at low cost for several challenging test cases. However, they rely on key properties of continuous-time systems that do not hold generally in discrete time. Nevertheless, we show that discrete-time analogues of these methods do provide valid enclosures for systems satisfying certain monotonicity conditions. We show that these conditions are always satisfied for systems obtained by forward Euler discretization of continuous-time models with step sizes below a computable upper limit. New refinement algorithms are presented for exploiting redundant model equations in the discrete-time setting. The resulting discrete-time DI methods are compared to existing algorithms using several case studies.