Data-Driven Estimation of Backward Reachable and Invariant Sets for Unmodeled Systems via Active Learning
Data-Driven Estimation of Backward Reachable and Invariant Sets for Unmodeled Systems via Active Learning
复制标题
通过主动学习对未建模系统的后向可达集和不变集进行数据驱动估计
DOI：
10.1109/cdc.2018.8619646
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
C. Danielson
中科院分区：
文献类型：
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作者：
A. Chakrabarty;A. Raghunathan;S. D. Cairano;C. Danielson
通过对可达集合和不变集合的理解，可以确保具有状态和输入约束的控制性能。虽然利用动力学模型提供了许多基于集合的算法来构建这些集合，但基于集合的方法通常不能很好地扩展，或者严重依赖于模型的精度或结构。相比之下，通过从允许的状态空间内采样的初始条件对复杂系统进行数值模拟，以数据驱动的方式生成状态轨迹相对简单，即使潜在的动力学完全未知。然后可以通过机器学习将这些样本用于可达/不变集估计，尽管学习性能与采样模式密切相关。本文采用主动学习的方法，通过子模块最大化的方法，智能地选择对已标注样本信息量最大、冗余度最小的样本批次。选择性采样减少了构造不变集估计器所需的数值模拟次数，从而增强了对高维状态空间的可伸缩性。通过一个数值算例说明了该框架的潜力。
Ensuring control performance with state and input constraints is facilitated by the understanding of reachable and invariant sets. While exploiting dynamical models have provided many set-based algorithms for constructing these sets, set-based methods typically do not scale well, or rely heavily on model accuracy or structure. In contrast, it is relatively simple to generate state trajectories in a data-driven manner by numerically simulating complex systems from initial conditions sampled from within an admissible state space, even if the underlying dynamics are completely unknown. These samples can then be leveraged for reachable/invariant set estimation via machine learning, although the learning performance is strongly linked to the sampling pattern. In this paper, active learning is employed to intelligently select batches of samples that are most informative and least redundant to previously labeled samples via submodular maximization. Selective sampling reduces the number of numerical simulations required for constructing the invariant set estimator, thereby enhancing scalability to higher-dimensional state spaces. The potential of the proposed framework is illustrated via a numerical example.