论文标题
输出反馈系统的线性二次高斯（LQG）控制的样品复杂性
Sample Complexity of Linear Quadratic Gaussian (LQG) Control for Output Feedback Systems
论文作者
论文摘要
本文研究了一类部分观察到的线性二次高斯（LQG）问题，但动态不明。我们建立了一个端到端样品复杂性，限制为开放环稳定植物的强大LQG控制器。这是使用可靠的合成过程实现的，在该过程中，我们首先从有限长度的单个输入输出轨迹中估算模型，确定在估计误差上绑定的H-互感，然后使用估计模型及其量化的不确定性设计强大的控制器。我们的综合过程利用了一个称为输入输出参数化（IOP）的最新控制工具，该工具可以使用凸优化实现强大的控制器设计。对于开环稳定系统，我们证明LQG性能使用所提出的合成过程对模型估计误差线性降低。尽管LQG问题中存在隐藏状态，但实现的缩放率与学习线性二次调节器（LQR）控制器的先前结果匹配具有完整状态观测值的结果。
This paper studies a class of partially observed Linear Quadratic Gaussian (LQG) problems with unknown dynamics. We establish an end-to-end sample complexity bound on learning a robust LQG controller for open-loop stable plants. This is achieved using a robust synthesis procedure, where we first estimate a model from a single input-output trajectory of finite length, identify an H-infinity bound on the estimation error, and then design a robust controller using the estimated model and its quantified uncertainty. Our synthesis procedure leverages a recent control tool called Input-Output Parameterization (IOP) that enables robust controller design using convex optimization. For open-loop stable systems, we prove that the LQG performance degrades linearly with respect to the model estimation error using the proposed synthesis procedure. Despite the hidden states in the LQG problem, the achieved scaling matches previous results on learning Linear Quadratic Regulator (LQR) controllers with full state observations.
