Optimal power management in wireless control systems

This paper considers the control of a linear plant when a sensor transmits plant state information over a wireless fading channel to a controller physically separated from the sensor. The power allocated to these transmissions determines the probability of successful reception and is adapted to channel and plant state in order to conserve the sensor´s energy resources. Our goal is to design plant control and power management policies to minimize an infinite horizon cost combining power consumption with the conventional linear quadratic regulator control cost. A method to separate the designs of plant inputs and transmitting powers is provided. The resulting optimal controller is the standard LQR control law while the optimal communication policy follows from a Markov decision process problem accounting for power at the sensor and state estimation error at the controller. The features of the optimal power management for general forward error correcting are examined qualitatively. In the particular case of transmissions protected with capacity achieving codes, conventional event-triggered policies are recovered, where the decision is whether to transmit or not. Further a suboptimal communication policy is computed using approximate dynamic programming and its behavior is validated in simulations and contrasted to other simple transmission policies.