On the Sample Complexity of Decentralized Linear Quadratic Regulator With Partially Nested Information Structure
On the Sample Complexity of Decentralized Linear Quadratic Regulator With Partially Nested Information Structure
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DOI：
10.1109/tac.2022.3215940
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发表时间：
2021-10
影响因子：
6.8
通讯作者：
Lintao Ye;Haoqi Zhu;V. Gupta
中科院分区：
文献类型：
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作者：
Lintao Ye;Haoqi Zhu;V. Gupta
本文研究在系统模型未知的情况下，具有部分嵌套信息结构的分散状态反馈线性二次控制的控制策略设计问题。我们提出了一种基于模型的学习解决方案，该方案包括两个步骤。首先，利用最小二乘估计，从有限长的单个系统轨迹估计未知系统模型。其次，基于估计的系统模型，设计了满足期望信息结构的分散控制策略。我们证明了我们的控制策略与最优分散控制策略(利用系统模型的准确知识设计)之间的次优差距与系统模型的估计误差成线性关系。利用这一结果，我们给出了具有部分嵌套信息结构的线性二次控制问题学习分散控制器的端到端样本复杂性结果。
In this article, we study the problem of control policy design for decentralized state-feedback linear quadratic control with a partially nested information structure, when the system model is unknown. We propose a model-based learning solution, which consists of two steps. First, we estimate the unknown system model from a single system trajectory of finite length, using least squares estimation. Next, based on the estimated system model, we design a decentralized control policy that satisfies the desired information structure. We show that the suboptimality gap between our control policy and the optimal decentralized control policy (designed using accurate knowledge of the system model) scales linearly with the estimation error of the system model. Using this result, we provide an end-to-end sample complexity result for learning decentralized controllers for a linear quadratic control problem with a partially nested information structure.