用深度神经算子融合反步法与强化学习，控制空间时变延迟的偏微分方程系统。
Neural Operator based Reinforcement Learning for Control of first-order PDEs with Spatially-Varying State Delay
- 用DeepONet构建可学习的反步控制器，替代传统固定延迟假设。
- 在仿真中优于无先验知识的SAC和解析控制器，收敛更快且鲁棒性更强。
- 适合需处理复杂空间依赖延迟的智能控制系统研究者。
受空间相关延迟影响的分布式参数系统控制极具挑战性，尤其当延迟随空间变化时。将解析控制理论与基于学习的控制方法统一于同一框架内，正展现出日益显著的优势。本文针对具有空间时变延迟的不稳定一阶双曲型偏微分方程（PDE），结合反步法控制策略与深度强化学习（RL）进行控制设计。为消除反步法设计中对延迟函数形式的强假设，提出一种融合DeepONet的软演员-评论家（SAC）架构，用于逼近反步控制器。DeepONet从反步控制器中提取特征，并输入至策略网络。仿真结果表明，该算法在性能上超越了无先验反步知识的基线SAC以及解析控制器。
原文摘要 · Abstract (English)
Control of distributed parameter systems affected by delays is a challenging task, particularly when the delays depend on spatial variables. The idea of integrating analytical control theory with learning-based control within a unified control scheme is becoming increasingly promising and advantageous. In this paper, we address the problem of controlling an unstable first-order hyperbolic PDE with spatially-varying delays by combining PDE backstepping control strategies and deep reinforcement learning (RL). To eliminate the assumption on the delay function required for the backstepping design, we propose a soft actor-critic (SAC) architecture incorporating a DeepONet to approximate the backstepping controller. The DeepONet extracts features from the backstepping controller and feeds them into the policy network. In simulations, our algorithm outperforms the baseline SAC without prior backstepping knowledge and the analytical controller.
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