Schemes for LQG Control over Gaussian Channels with Side Information

We consider the problem of controlling an unstable scalar linear plant over a power-constrained additive white Gaussian noise (AWGN) channel, where the controller/receiver has access to an additional noisy measurement of the state of the control system. To that end, we view the noisy measurement as side information and recast the problem to that of joint source-channel coding with side information at the receiver. We argue that judicious modulo-based schemes improve over their linear counterparts and allow to avoid a large increase in the transmit power due to the ignorance of the side information at the sensor/transmitter. We demonstrate the usefulness of our technique for the settings where i) the sensor is oblivious of the control objectives, control actions and previous controller state estimates, ii) the system output tracks a desired reference signal that is available only at the controller via integral control action.