Encoder-decoder design for feedback control over the binary symmetric channel

Encoder-decoder design is considered for a closed-loop scalar control system with feedback transmitted over a binary symmetric channel. We propose an iterative procedure which can jointly optimize adaptive encoder-decoder pairs for a certainly equivalence controller. The goal is to minimize a design criterion, in particular, the linear quadratic (LQ) cost function over a finite horizon. The algorithm leads to a practically feasible design of time-varying non-uniform encoding and decoding. Numerical results demonstrate the promising performance obtained by employing the proposed iterative optimization algorithm.