论文标题
数据驱动的线性系统的安全控制在认知和造成的不确定性下
Data-driven Safe Control of Linear Systems Under Epistemic and Aleatory Uncertainties
论文作者
论文摘要
考虑了在认知和造成的不确定性下对约束线性系统的安全控制。不确定性的不确定性表征了随机噪声，并以概率分布函数（PDF）进行建模，而认知不确定性则表征了对系统动力学的知识。基于数据的概率安全控制器是针对噪声PDF为1）具有已知协方差的零均值高斯的情况，2）零均值高斯具有不确定的协方差； 3）零均值的非高斯零均高斯，分布不明。通过引入概率的承包集，为第一种情况提供了易于检查的基于基于模型的模型，以确保概率安全。然后，通过分别利用基于分布的概率安全控制和有条件的概率概率安全控制，将这些结果扩展到第二和第三个情况。然后考虑基于数据的这些概率安全控制器的实现。结果表明，直接学习的数据填充要求比对实现模型识别的基于模型的安全控制方法的数据填充要求要弱得多。此外，使用收集到的数据学会了最小风险水平的上限，并保证了安全控制器的存在。提供了一个模拟示例，以显示提出的方法的有效性。
Safe control of constrained linear systems under both epistemic and aleatory uncertainties is considered. The aleatory uncertainty characterizes random noises and is modeled by a probability distribution function (PDF) and the epistemic uncertainty characterizes the lack of knowledge on the system dynamics. Data-based probabilistic safe controllers are designed for the cases where the noise PDF is 1) zero-mean Gaussian with a known covariance, 2) zero-mean Gaussian with an uncertain covariance, and 3) zero-mean non-Gaussian with an unknown distribution. Easy-to-check model-based conditions for guaranteeing probabilistic safety are provided for the first case by introducing probabilistic contractive sets. These results are then extended to the second and third cases by leveraging distributionally-robust probabilistic safe control and conditional value-at-risk (CVaR) based probabilistic safe control, respectively. Data-based implementations of these probabilistic safe controllers are then considered. It is shown that data-richness requirements for directly learning a safe controller is considerably weaker than data-richness requirements for model-based safe control approaches that undertake a model identification. Moreover, an upper bound on the minimal risk level, under which the existence of a safe controller is guaranteed, is learned using collected data. A simulation example is provided to show the effectiveness of the proposed approach.
