Data-Driven Reachability Analysis with Christoffel Functions
Data-Driven Reachability Analysis with Christoffel Functions
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DOI：
10.1109/cdc45484.2021.9682860
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发表时间：
2021-04
期刊：
影响因子：
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通讯作者：
Alex Devonport;Forest Yang;L. Ghaoui;M. Arcak
中科院分区：
文献类型：
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作者：
Alex Devonport;Forest Yang;L. Ghaoui;M. Arcak
我们提出了一种算法，数据驱动的可达性分析，估计有限的地平线向前可达的一般非线性系统使用子水平集的某一类多项式称为经验逆Christoffel函数，这是已知的经验，以提供良好的近似概率分布的支持。该算法使用此属性的可达性分析，解决了概率松弛的可达集计算问题。我们还提供了一个保证，该算法的输出是一个准确的可达集近似在概率意义上，只要达到一定的样本量。我们还研究了三个数值例子来证明算法的能力，如提供非凸可达集近似和检测可达集中的漏洞。
We present an algorithm for data-driven reachability analysis that estimates finite-horizon forward reachable sets for general nonlinear systems using sub-level sets of a certain class of polynomials known as empirical inverse Christoffel functions, which are known empirically to provide good approximations to the support of probability distributions. The algorithm uses this property for reachability analysis by solving a probabilistic relaxation of the reachable set computation problem. We also provide a guarantee that the output of the algorithm is an accurate reachable set approximation in a probabilistic sense, provided that a certain sample size is attained. We also investigate three numerical examples to demonstrate the algorithm’s capabilities, such as providing non-convex reachable set approximations and detecting holes in the reachable set.