Synthesis of Simple Feed-Forward Networks: A First-Order Example

Stability analysis of networks has been the focus of much research over the past decade. Presently, researchers are investigating performance and synthesis of controllers and channel coding schemes in networks. Such design problems are difficult in general, as there is a strong interplay between control objectives and communication constraints, which forces the synthesis of controllers and channel encoders to be done simultaneously. Current approaches typically fix one, while the other is designed to meet some objective. In this paper, we consider a simple network, in which the plant and controller are local to each other, but are together driven by a remote reference signal that is transmitted through a noisy discrete channel. We first construct a model matching performance metric that captures the tradeoffs between coding the reference command to achieve more accuracy at the remote site and designing a controller to meet performance. We then simultaneously synthesize the controller and encoder block lengths that meet the specified objective for a first-order plant and model case. Finally, we illustrate performance sensitivity to the poles of the plant and model, and to the channel noise.