论文标题
使用Wasserstein度量的最小值控制线性随机系统
Minimax control of ambiguous linear stochastic systems using the Wasserstein metric
论文作者
论文摘要
在本文中，我们提出了一种最小值线性二次控制方法，以解决实际随机系统中分布信息不准确的问题。为了构建一种反对不确定性的经验分布中错误的控制策略，我们的方法是采用对手，该对手选择最差的分布。为了系统地调整我们方法的保守性，对手获得了与瓦斯坦斯坦度量标准衡量的数量成正比的罚款，偏离了经验分布。在有限的horizon情况下，使用riccati方程式，我们得出了独特的最佳策略的封闭式表达，以及产生最坏情况分布的对手的策略。然后，通过识别Riccati递归在将唯一阳性半明确溶液收敛到相关的代数riccati方程（AS）的条件下，将此结果扩展到无限 - 水平的设置。结果显示，最佳策略可在最差的分布下稳定系统状态的预期价值。我们还讨论了我们的方法可以解释为$ h_ \ infty $ -Method的分布概括。
In this paper, we propose a minimax linear-quadratic control method to address the issue of inaccurate distribution information in practical stochastic systems. To construct a control policy that is robust against errors in an empirical distribution of uncertainty, our method is to adopt an adversary, which selects the worst-case distribution. To systematically adjust the conservativeness of our method, the opponent receives a penalty proportional to the amount, measured with the Wasserstein metric, of deviation from the empirical distribution. In the finite-horizon case, using a Riccati equation, we derive a closed-form expression of the unique optimal policy and the opponent's policy that generates the worst-case distribution. This result is then extended to the infinite-horizon setting by identifying conditions under which the Riccati recursion converges to the unique positive semi-definite solution to an associated algebraic Riccati equation (ARE). The resulting optimal policy is shown to stabilize the expected value of the system state under the worst-case distribution. We also discuss that our method can be interpreted as a distributional generalization of the $H_\infty$-method.
