UC San Diego

This thesis deals with a single feedback fixed-rate channel using some coding strategies. We assess and compare the LQ performance of the different coding methods. The idea of predictive coding is applied at the transmitter side to improve the efficiency of the channel usage by transmission of the quantized innovations signal. We observe a plant stability requirement is necessary to construct the joint density of both the plant and the predictor states at the receiver side. The Bayesian filter is used to compute the optimal feedback control. We compare the closed-loop control performance for three cases. In each of these competing cases, a lower complexity receiver architecture is possible but at the expense of closed-loop control performance.

In addition to predictive coding, we examine specific low-bitrate strategies and

evaluate through their impact on LQ control performance. We consider coding the quantized output signal deploying period-two codes of differing delay versus accuracy tradeoff. We treat the quantizer as the functional composition of an infinitely-long linear staircase function and a saturation. This permits the analysis being subdivided into estimator computations and an escape time evaluation, which connects the control back into the choice of quantizer saturation bound. By limiting the subject to specific strategies, we are able to identify principles underlying coding for control.