This paper addresses the distributed online control problem over a network of linear time-invariant (LTI) systems (with possibly unknown dynamics) in the presence of adversarial perturbations. There exists a global network cost that is characterized by a time-varying convex function, which evolves in an adversarial manner and is sequentially and partially observed by local agents. The goal of each agent is to generate a control sequence that can compete with the best centralized control policy in hindsight, which has access to the global cost. This problem is formulated as a regret minimization. For the case of known dynamics, we propose a fully distributed disturbance feedback controller that guarantees a regret bound of $O(\sqrt{T}\log T)$, where $T$ is the time horizon. For the unknown dynamics case, we design a distributed explore-then-commit approach, where in the exploration phase all agents jointly learn the system dynamics, and in the learning phase our proposed control algorithm is applied using each agent system estimate. We establish a regret bound of $O(T^{2/3} \text{poly}(\log T))$ for this setting.

本研究解决了分布式在线控制问题，考虑了存在对抗干扰的线性时不变系统网络。针对已知动态和未知动态两种情况，分别提出了全分布式干扰反馈控制器和探索-执行方法，并给出了相应的遗憾界。

具有对抗性干扰的线性时不变系统分布式在线控制的遗憾分析