SIAM Journal on Control and Optimization, Volume 58, Issue 5, Page 2927-2951, January 2020.
In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear time-invariant systems. By leveraging modern techniques in distributed controller synthesis and structured linear inverse problems as applied to system identification, we show that near-optimal distributed controllers can be learned with sublinear sample complexity and computed with near-linear time complexity, both measured with respect to the dimension of the system. In particular, we provide sharp end-to-end guarantees on the stability and the performance of the designed distributed controller and prove that for sparse systems, the number of samples needed to guarantee robust and near optimal performance of the designed controller can be significantly smaller than the dimension of the system. Finally, we show that the proposed optimization problem can be solved to global optimality with near-linear time complexity by iteratively solving a series of small quadratic programs.

中文翻译：

---

分布式线性二次控制策略的有效学习

SIAM控制与优化杂志，第58卷，第5期，第2927-2951页，2020年1月。
在这项工作中，我们提出了一种健壮的方法来为未知但稀疏的线性时不变系统设计分布式控制器。通过利用分布式控制器综合中的现代技术以及应用于系统识别的结构化线性逆问题，我们表明可以通过亚线性样本复杂度学习近似最优的分布式控制器，并可以通过近似线性时间复杂度来计算近似最优的分布式控制器，两者均相对于维度进行了测量系统的。特别是，我们为所设计的分布式控制器的稳定性和性能提供了端到端的严格保证，并证明对于稀疏系统，为保证所设计的控制器的鲁棒性和接近最佳性能所需的样本数量可以大大减少。比系统的尺寸大。最后，