Data-Driven Reachable Set Computation using Adaptive Gaussian Process Classification and Monte Carlo Methods
Data-Driven Reachable Set Computation using Adaptive Gaussian Process Classification and Monte Carlo Methods
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DOI：
10.23919/acc45564.2020.9147918
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发表时间：
2019-10
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通讯作者：
Alex Devonport;M. Arcak
中科院分区：
文献类型：
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作者：
Alex Devonport;M. Arcak
提出了两种数据驱动的估计概率保证可达集的方法。这两种方法都使用概率公式，允许对数据驱动的可达集近似值进行正式定义，该近似值在概率意义上是正确的。第一种方法将可达性问题转换为二值分类问题，使用高斯过程分类器表示可达集。高斯过程模型的量化不确定性允许自适应方法来选择新的样本点。第二种方法使用蒙特卡罗采样方法来计算可达集的基于区间的近似值。该方法保证了概率的正确性，并明确规定了实现所需精度和置信度所需的样本点数量。每种方法都用一个数值例子加以说明。
We present two data-driven methods for estimating reachable sets with probabilistic guarantees. Both methods make use of a probabilistic formulation allowing for a formal definition of a data-driven reachable set approximation that is correct in a probabilistic sense. The first method recasts the reachability problem as a binary classification problem, using a Gaussian process classifier to represent the reachable set. The quantified uncertainty of the Gaussian process model allows for an adaptive approach to the selection of new sample points. The second method uses a Monte Carlo sampling approach to compute an interval-based approximation of the reachable set. This method comes with a guarantee of probabilistic correctness, and an explicit bound on the number of sample points needed to achieve a desired accuracy and confidence. Each method is illustrated with a numerical example.