We focus on the control of unknown Partial Differential Equations (PDEs). The system dynamics is unknown, but we assume we are able to observe its evolution for a given control input, as typical in a Reinforcement Learning framework. We propose an algorithm based on the idea to control and identify on the fly the unknown system configuration. In this work, the control is based on the State-Dependent Riccati approach, whereas the identification of the model on Bayesian linear regression. At each iteration, based on the observed data, we obtain an estimate of the a-priori unknown parameter configuration of the PDE and then we compute the control of the correspondent model. We show by numerical evidence the convergence of the method for infinite horizon control problems.

翻译：本文聚焦于未知偏微分方程（PDEs）的控制问题。系统动力学未知，但我们假设能够观测其在给定控制输入下的演化过程，这符合强化学习框架的典型设定。我们提出一种基于在线控制与辨识未知系统配置思想的算法。本工作中，控制采用状态依赖Riccati方法，而模型辨识则基于贝叶斯线性回归。每次迭代中，基于观测数据获得偏微分方程先验未知参数配置的估计值，继而计算对应模型的控制律。通过数值实验证明了该方法在无限时域控制问题中的收敛性。