arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2103.01413cs.LGcs.SYeess.SYmath.OCstat.ML
收藏

不确定环境下的安全学习

Safe Learning of Uncertain Environments

University of Melbourne(墨尔本大学);Defence Science and Technology Group(国防科学技术集团);Australian National University(澳大利亚国立大学)

Farhad Farokhi, Alex Leong, Iman Shames, Mohammad Zamani

摘要:

在许多基于学习的控制方法中,学习未知的动态模型先于控制阶段,而目的是控制系统,使其保持在状态空间的某个安全区域。在这项工作中,我们的目标是在学习和控制同时进行的同时保证安全。具体来说,我们考虑的问题,安全学习的非线性控制仿射系统的未知添加剂的不确定性。我们首先将不确定性建模为高斯噪声,并使用状态测量来学习其均值和协方差。我们提供严格的时变界限的不确定性的均值和协方差,并采用它们来修改控制输入通过一个优化程序与潜在的时变安全约束。我们表明,以任意大的概率,我们可以保证状态将保持在安全集,而学习和控制同时进行,提供了一个可行的解决方案存在的优化问题。我们提供了一个二次配方的这种优化,是计算上更有效。这是基于收紧安全约束,以对抗学习均值和协方差的不确定性。收紧的幅度可以随着我们对学习均值和协方差的信心增加而减小(即,当我们收集更多关于环境的测量时)。扩展的方法提供了未知的均值和协方差的非高斯过程噪声,以及高斯不确定性与状态相关的均值和协方差,以适应更一般的环境。

英文摘要:

In many learning based control methodologies, learning the unknown dynamic model precedes the control phase, while the aim is to control the system such that it remains in some safe region of the state space. In this work, our aim is to guarantee safety while learning and control proceed simultaneously. Specifically, we consider the problem of safe learning in nonlinear control-affine systems subject to unknown additive uncertainty. We first model the uncertainty as a Gaussian noise and use state measurements to learn its mean and covariance. We provide rigorous time-varying bounds on the mean and covariance of the uncertainty and employ them to modify the control input via an optimization program with potentially time-varying safety constraints. We show that with an arbitrarily large probability we can guarantee that the state will remain in the safe set, while learning and control are carried out simultaneously, provided that a feasible solution exists for the optimization problem. We provide a secondary formulation of this optimization that is computationally more efficient. This is based on tightening the safety constraints to counter the uncertainty about the learned mean and covariance. The magnitude of the tightening can be decreased as our confidence in the learned mean and covariance increases (i.e., as we gather more measurements about the environment). Extensions of the method are provided for non-Gaussian process noise with unknown mean and covariance as well as Gaussian uncertainties with state-dependent mean and covariance to accommodate more general environments.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑