Coded Control over Lossy Networks

Ye Pu, Jingge Zhu, Karl Henrik Johansson, Kannan Ramchandran, Claire J. Tomlin

Abstract: We consider a networked control system with an unreliable feedback link from the sensor to the controller. Specifically, a discrete-time linear system is to be controlled via a packet-drop channel where multiple packets are transmitted at each time instance. We propose a coded control scheme that jointly designs the coding strategy, which mitigates the channel unreliability, and the control strategy, which stabilizes the unstable system. This scheme is based on the idea of successive refinement, that more important system states (or linear combinations thereof) should be better protected against the unreliable channel. The proposed scheme is simple to implement as it uses a static encoder and decoder/controller, in the sense that all encoding and decoding procedures do not require information from previous time steps. Furthermore, we compare it with two other static schemes and show that our approach strikes a good balance between optimality and complexity.