提出分布式在线控制的谱滤波方法，实现近最优性能。
A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systems
- 用谱控制器结合邻居通信，动态调整控制策略。
- 在对抗干扰下达到子线性后悔界 $O( rac{\sqrt{T} ext{poly}(\log T)}{ ^3})$。
- 适合多智能体系统实时控制，尤其关注稳定性与网络结构。
本文研究在对抗性扰动和时变凸代价下，由线性时不变（LTI）系统组成的网络中的分布式在线控制问题。网络总代价为各局部代价函数之和，每个局部代价仅对对应代理可见。各代理的目标是仅基于本地观测和邻域通信，生成一个控制序列，以竞争于事后最优的集中式线性策略。本文将近期提出的在线谱控制框架拓展至分布式场景：每个代理通过卷积历史扰动与汉克尔矩阵主特征向量获得谱控制器，控制器参数通过局部代理成本的分布式在线梯度下降更新。该问题被形式化为基于谱参数化的后悔最小化问题，在标准假设下，建立了子线性后悔界 $O( rac{\sqrt{T} ext{poly}(\log T)}{ ^3})$，其中 $T$ 为时间范围，$ $ 表示稳定裕度。该结果还捕捉了网络规模与连通性的影响。
原文摘要 · Abstract (English)
This paper studies the distributed online control problem over a network of linear time-invariant (LTI) systems in the presence of adversarial disturbances and time-varying convex costs. The network cost is characterized by the summation of local cost functions, where each local function is sequentially revealed only to the corresponding agent. The goal of each agent is to generate a control sequence, using only local observations and neighbor communication, that competes with the best {\it centralized} linear policy in hindsight. We extend the recently proposed Online Spectral Control framework from the centralized setting to the distributed setting. In particular, each agent applies a spectral controller obtained by convolving past disturbances with the leading eigenvectors of a Hankel matrix, while the controller parameters are updated through a distributed online gradient descent step over the local surrogate costs. We formulate this problem this problem as a {\it regret} minimization problem based on the spectral parameterization, and under standard assumptions, we establish a sublinear regret bound of $O(\frac{\sqrt{T}\text{poly}(\log T)}{γ^3})$, where $T$ is the time horizon and $γ$ denotes the stability margin. The resulting bound also captures the dependence on the network size and connectivity.
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