Poisson Networked Control Systems: Statistical Analysis and Online Learning for Channel Access

We develop a framework for communication-control co-design in a wireless networked control system with multiple geographically separated controllers and controlled systems. Each controlled system consists of an actuator, plant, and sensor. The locations of the controller-controlled system pairs are modeled using a Poisson point process. Controllers periodically receive system state estimates from their respective sensors and design control inputs accordingly. The inputs are then communicated to the corresponding actuators over a shared wireless channel, leading to interference. Our co-design includes a control strategy at the controller based on sensor measurements and transmission acknowledgments from the actuators, utilizing a block ALOHA protocol for channel access. First, we provide a statistical analysis of the control performance. Then, we introduce a Thompson sampling-based online learning algorithm to optimize channel access via the ALOHA parameter. Finally, our numerical results demonstrate the impact of the choice of the ALOHA parameter on the control performance and the efficacy of the learning algorithm in choosing the optimal ALOHA parameter.