论文标题
遗憾的分析风险感知线性二次控制
Regret Analysis for Risk-aware Linear Quadratic Control
论文作者
论文摘要
本文调查了与分布稳健控制（DRC）策略相关的遗憾，用于解决多阶段优化问题，在这些问题中，涉及的概率分布尚不确切，而是假定属于指定的歧义家庭。我们量化了价格（分配遗憾），即一个人最终因不知道随机系统不确定性的确切概率分布而付出代价，同时旨在使用DRC策略来控制它。刚果民主共和国策略在被认为是歧义集中最坏情况下的不确定性分布的保守主义是以缺乏有关该集合中真正分布的知识的代价。我们使用最糟糕的情况有条件的危险案例来定义分布遗憾，并且发现遗憾随着风险更高的水平而增加。本文的动机是促进新的控制算法的设计，以最大程度地减少分销遗憾。
This paper investigates the regret associated with the Distributionally Robust Control (DRC) strategies used to address multistage optimization problems where the involved probability distributions are not known exactly, but rather are assumed to belong to specified ambiguity families. We quantify the price (distributional regret) that one ends up paying for not knowing the exact probability distribution of the stochastic system uncertainty while aiming to control it using the DRC strategies. The conservatism of the DRC strategies for being robust to worst-case uncertainty distribution in the considered ambiguity set comes at the price of lack of knowledge about the true distribution in the set. We use the worst case Conditional Value-at-Risk to define the distributional regret and the regret bound was found to be increasing with tighter risk level. The motive of this paper is to promote the design of new control algorithms aiming to minimize the distributional regret.
