Rate allocation for quantized control over noisy channels

To achieve satisfactory overall performance, optimal rate allocation in a networked control system with highly limited communication resources is instrumental. In this paper, a rate allocation technique for state feedback control in linear dynamic systems over a noisy channel is proposed. The method consists of two steps: (i) the overall cost is expressed as a function of rates at all time instants by means of high-rate quantization theory, and (ii) a constrained optimization problem to minimize the overall distortion is solved. It is shown that a non-uniform quantization is in general the best strategy for state feedback control over noisy channels. Monte Carlo simulations illustrate the proposed scheme, which is shown to have good performance when compared to arbitrarily selected rate allocations.