The design of Wireless Networked Control System (WNCS) requires addressing critical interactions between control and communication systems with minimal complexity and communication overhead while providing ultra-high reliability. This paper introduces a novel optimization theory based deep reinforcement learning (DRL) framework for the joint design of controller and communication systems. The objective of minimum power consumption is targeted while satisfying the schedulability and rate constraints of the communication system in the finite blocklength regime and stability constraint of the control system. Decision variables include the sampling period in the control system, and blocklength and packet error probability in the communication system. The proposed framework contains two stages: optimization theory and DRL. In the optimization theory stage, following the formulation of the joint optimization problem, optimality conditions are derived to find the mathematical relations between the optimal values of the decision variables. These relations allow the decomposition of the problem into multiple building blocks. In the DRL stage, the blocks that are simplified but not tractable are replaced by DRL. Via extensive simulations, the proposed optimization theory based DRL approach is demonstrated to outperform the optimization theory and pure DRL based approaches, with close to optimal performance and much lower complexity.

翻译：无线网络化控制系统（WNCS）的设计需要在实现超高可靠性的同时，以最小的复杂性和通信开销解决控制与通信系统之间的关键交互问题。本文提出了一种基于优化理论的深度强化学习（DRL）框架，用于控制器与通信系统的联合设计。目标是在满足有限码长体制下通信系统的可调度性约束、速率约束以及控制系统的稳定性约束的前提下，实现最小功耗。决策变量包括控制系统的采样周期，以及通信系统的码长和误包概率。该框架包含两个阶段：优化理论阶段和DRL阶段。在优化理论阶段，通过构建联合优化问题，推导出最优性条件以揭示决策变量最优值之间的数学关系，从而将问题分解为多个基础模块。在DRL阶段，将简化但难以解析求解的模块替换为DRL方法。大量仿真结果表明，所提出的基于优化理论的DRL方法在接近最优性能且复杂度显著降低的条件下，优于纯优化理论方法和纯DRL方法。