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：无线网络控制系统（WNCS）的设计需要在最小化复杂度和通信开销的同时解决控制与通信系统之间的关键交互，并提供超高可靠性。本文提出了一种基于优化理论的深度强化学习（DRL）新框架，用于控制器和通信系统的联合设计。在满足有限块长机制下通信系统的可调度性和速率约束以及控制系统的稳定性约束的同时，以最小化功率消耗为目标。决策变量包括控制系统的采样周期，以及通信系统的块长和分组错误概率。所提框架包含两个阶段：优化理论和深度强化学习。在优化理论阶段，在制定联合优化问题后，推导出最优条件以寻找决策变量最优值之间的数学关系。这些关系允许将问题分解为多个构建模块。在深度强化学习阶段，将简化但难以处理的模块替换为深度强化学习。通过大量仿真，所提出的基于优化理论的深度强化学习方法被证明优于基于纯优化理论和纯深度强化学习的方法，具有接近最优的性能和更低的复杂度。