Optimal design of remote controllers for LTI plants over erasure channels ⋆

In this paper we consider the remote control of a noisy linear time-invariant (LTI) plant over erasure channels located in both the plant-to-controller and controller-to-plant links. We restrict our attention to a class of controllers where all processing is affine, except for some elementary use of sensor-to-controller channel state information. For such controller class, we show that optimal designs separate into an estimation and a state feedback design problem when perfect packet acknowledgements are available at the controller. Interestingly, our results also show that the affine part of the controller converges, as the time goes to infinity, to an LTI filter under the same conditions which guarantee mean-square stability in the well-known LQG control problem over erasure channels. However, our infinite horizon proposal is computationally inexpensive and its steady-state behaviour can be characterized straightforwardly.