We study the problem of adaptive control in partially observable linear dynamical systems. We propose a novel algorithm, adaptive control online learning algorithm (AdaptOn), which efficiently explores the environment, estimates the system dynamics episodically and exploits these estimates to design effective controllers to minimize the cumulative costs. Through interaction with the environment, AdaptOn deploys online convex optimization to optimize the controller while simultaneously learning the system dynamics to improve the accuracy of controller updates. We show that when the cost functions are strongly convex, after $T$ times step of agent-environment interaction, AdaptOn achieves regret upper bound of $\text{polylog}\left(T\right)$. To the best of our knowledge, AdaptOn is the first algorithm which achieves $\text{polylog}\left(T\right)$ regret in adaptive control of unknown partially observable linear dynamical systems which includes linear quadratic Gaussian (LQG) control.

研究如何在部分可观测线性动态系统中进行系统识别和自适应控制，提出了一种基于模型评估的自适应控制在线学习算法，可通过与环境的交互来估计模型动态，通过在线梯度下降更新控制器并改善控制器效能，该算法达到了未知系统的自适应控制的Polylog(T)的遗憾上限。

部分可观察线性动力系统的对数遗憾界