论文标题
Wasserstein分布对部分可观察的线性随机系统的分布强大的控制
Wasserstein Distributionally Robust Control of Partially Observable Linear Stochastic Systems
论文作者
论文摘要
分布稳健的控制（DRC）旨在有效地管理随机系统中的分布歧义。尽管大多数现有的作品都解决了完全可观察到的设置中的不准确分布信息，但我们考虑使用Wasserstein Metric的离散时间线性系统的部分可观察到的DRC问题。对于可拖动的解决方案，我们提出了一种新型的近似方法，利用了瓦斯汀距离的胶状结构。使用现代分布强劲优化的技术，我们为最佳控制策略提供了封闭形式的表达，并且在有限的 - 摩尼斯和Infinite-Horizon平均成本设置中，对于最差的案例分布策略，可拖动的半决赛编程问题。提出的方法具有多种显着的理论属性，例如保证的成本属性和概率的样本外部性能保证，证明了我们控制器的分布鲁棒性。此外，显示的控制器被证明可确保均值系统的闭环稳定性。通过有关功率系统频率控制问题的数值实验，我们的方法的经验性能进行了测试。
Distributionally robust control (DRC) aims to effectively manage distributional ambiguity in stochastic systems. While most existing works address inaccurate distributional information in fully observable settings, we consider a partially observable DRC problem for discrete-time linear systems using the Wasserstein metric. For a tractable solution, we propose a novel approximation method exploiting the Gelbrich bound of Wasserstein distance. Using techniques from modern distributionally robust optimization, we derive a closed-form expression for the optimal control policy and a tractable semidefinite programming problem for the worst-case distribution policy in both finite-horizon and infinite-horizon average-cost settings. The proposed method features several salient theoretical properties, such as a guaranteed cost property and a probabilistic out-of-sample performance guarantee, demonstrating the distributional robustness of our controller. Furthermore, the resulting controller is shown to ensure the closed-loop stability of the mean-state system. The empirical performance of our method is tested through numerical experiments on a power system frequency control problem.
