Minimum-energy packet forwarding policies for guaranteed LQG performance in wireless control systems

This paper studies minimum-energy packet forwarding policies for communicating sensor measurements from plant to controller over an unreliable multi-hop wireless network so as to guarantee that the optimal controller achieves a prespecified closed-loop performance. For fixed sampling interval, we demonstrate that the minimal linear-quadratic control loss is monotonically decreasing in the reliability of the sensor-to-controller communication. This allows us to decompose the overall design problem into two separate tasks: finding the minimum end-to-end reliability that allows to achieve a prespecified linear-quadratic loss, and developing minimum-energy packet forwarding policies under a deadline-constrained reliability requirement. We develop optimal solutions for both subproblems and show how the co-designed system with minimum forwarding energy cost and guaranteed LQG control performance can be found by a one-dimensional search over admissible sampling periods. The paper ends with a numerical example which demonstrates the effectiveness of the proposed framework.