Optimal Power Management in Wireless Control Systems

This paper considers the control of a linear plant when plant state information is being transmitted from a sensor to the controller over a wireless fading channel. The power allocated to these transmissions determines the probability of successful packet reception and is allowed to adapt online to both channel conditions and plant state. The goal is to design plant input and transmit power policies that minimize an infinite horizon cost combining power expenses and the conventional linear quadratic regulator control cost. Since plant inputs and transmit powers are in general coupled, a restricted information structure is imposed allowing them to be designed separately. Under this information structure the standard LQR controller becomes the optimal plant input policy, while the optimal communication policy follows a Markov decision process minimizing transmit power at the sensor and state estimation error at the controller. The optimal power adaptation to channel and plant states is examined qualitatively for general forward error correcting codes. In the particular case of capacity achieving codes event-triggered policies are recovered, where the sensor decides whether to transmit or not based on plant and channel conditions. Approximate dynamic programming is employed to derive a family of tractable suboptimal communication policies exhibiting the same qualitative features as the optimal one. The performance of our suboptimal policies is shown in simulations and is contrasted to other simple transmission policies.