Minimum Energy Data Transmission for Wireless Networked Control Systems

The communication protocol design for wireless networked control systems brings the additional challenge of providing the guaranteed stability of the closed-loop control system compared to traditional wireless sensor networks. In this paper, we provide a framework for the joint optimization of controller and communication systems encompassing efficient abstractions of both systems. The objective of the optimization problem is to minimize the power consumption of the communication system due to the limited lifetime of the battery-operated wireless nodes. The constraints of the problem are the schedulability and maximum transmit power restrictions of the communication system, and the reliability and delay requirements of the control system to guarantee its stability. The formulation comprises communication system parameters including transmission power, rate and scheduling, and control system parameters including sampling period. The resulting problem is a Mixed-Integer Programming problem. However, analyzing the optimality conditions on the variables of the problem allows us to reduce it to an Integer Programming problem for which we propose an efficient solution method based on its relaxation. Simulations demonstrate that the proposed method performs very close to optimal and much better than the traditional separate design of these systems.