Sampled-Data Reachability Analysis Using Sensitivity and Mixed-Monotonicity
Sampled-Data Reachability Analysis Using Sensitivity and Mixed-Monotonicity
复制标题
使用灵敏度和混合单调性的采样数据可达性分析
DOI：
10.1109/lcsys.2018.2848280
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发表时间：
2018
影响因子：
3
通讯作者：
M. Arcak
中科院分区：
文献类型：
--
作者：
Pierre;S. Coogan;M. Arcak
这封信过近似的可达集的连续时间不确定系统使用的灵敏度，其轨迹相对于初始条件和不确定参数。我们首先证明了现有的过度近似结果的基础上的灵敏度矩阵的符号稳定性和依赖于混合单调性的离散时间方法之间的等价性。然后，我们提出了一个新的过度近似的结果，在最坏的线性状态的尺寸，并适用于任何连续时间系统的有界灵敏度。最后，我们提供了一个基于模拟的方法来估计这些界限，通过采样和证伪。最后，以交通网络和卫星轨道为例，说明了本文的结果。
This letter over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing over-approximation result based on the sign-stability of the sensitivity matrices and a discrete-time approach relying on a mixed-monotonicity property. We then present a new over-approximation result which scales at worst linearly with the state dimension and is applicable to any continuous-time system with bounded sensitivity. Finally, we provide a simulation-based approach to estimate these bounds through sampling and falsification. The results are illustrated with numerical examples on traffic networks and satellite orbits.