Networked Control with Hybrid Automatic Repeat Request Protocols

We study feedback control of a dynamical process over a lossy channel equipped with a hybrid automatic repeat request protocol that connects a sensor to an actuator. The dynamical process is modeled by a Gauss-Markov process, and the lossy channel by a packet-erasure channel with ideal feedback. We suppose that data is communicated in the format of packets with negligible quantization error. In such a networked control system, whenever a packet loss occurs, there exists a tradeoff between transmitting new sensory information with a lower success probability and retransmitting previously failed sensory information with a higher success probability. In essence, an inherent tradeoff between freshness and reliability. To address this tradeoff, we consider a linear-quadratic-regulator performance index, which penalizes state deviations and control efforts over a finite horizon, and jointly design optimal policies for an encoder and a decoder, which are collocated with the sensor and the actuator, respectively. Our emphasis here lies specifically on designing switching and control policies, rather than error-correcting codes. We derive the structural properties of the optimal encoding and decoding policies. We show that the former is a threshold switching policy and the latter is a certainty-equivalent control policy. In addition, we specify the iterative equations that the encoder and the decoder need to solve in order to implement the optimal policies.