A dynamic game approach to distributionally robust safety specifications for stochastic systems
A dynamic game approach to distributionally robust safety specifications for stochastic systems
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DOI：
10.1016/j.automatica.2018.04.022
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发表时间：
2017-01
期刊：
影响因子：
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通讯作者：
Insoon Yang
中科院分区：
文献类型：
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作者：
Insoon Yang
本文提出了一种新的安全规格方法，对干扰概率分布中的误差具有鲁棒性。我们提出的分布式鲁棒安全策略最大限度地提高了系统始终保持在所需集合中的概率，但在模糊集合中存在最坏的干扰分布。我们提出了一个动态的游戏制定建设这样的政策，并确定条件下，非随机马尔可夫政策是最佳的。基于这个存在性结果，我们开发了一个实用的设计方法，以安全为导向的随机控制器的有限信息的干扰分布。然而，一个相关的贝尔曼方程涉及无限维极大极小优化问题，因为扰动分布可能具有连续的密度。为了减轻计算问题，我们提出了一个基于对偶的重构方法，将无限维极大极小问题转化为一个半无限的程序，可以使用现有的收敛算法来解决。我们证明，没有对偶差距，这种方法，从而保持最优性。数值试验的结果证实，所提出的方法是强大的分布误差的干扰，而一个标准的随机安全验证工具。
This paper presents a new safety specification method that is robust against errors in the probability distribution of disturbances. Our proposed distributionally robust safe policy maximizes the probability of a system remaining in a desired set for all times, subject to the worst possible disturbance distribution in an ambiguity set. We propose a dynamic game formulation of constructing such policies and identify conditions under which a non-randomized Markov policy is optimal. Based on this existence result, we develop a practical design approach to safety-oriented stochastic controllers with limited information about disturbance distributions. However, an associated Bellman equation involves infinite-dimensional minimax optimization problems since the disturbance distribution may have a continuous density. To alleviate computational issues, we propose a duality-based reformulation method that converts the infinite-dimensional minimax problem into a semi-infinite program that can be solved using existing convergent algorithms. We prove that there is no duality gap, and that this approach thus preserves optimality. The results of numerical tests confirm that the proposed method is robust against distributional errors in disturbances, while a standard stochastic safety verification tool is not.