Optimal tracking and power allocation over AWN feedback channels

In this chapter, we study the fundamental limitations of multi-input, multi-output (MIMO) networked feedback systems in tracking reference input signals. We adopt an additive white noise (AWN) model for the communication channel, and consider as our performance measure the mean-square error for a system's output to track a random signal with finite power. We show that in this setting the AWN channel power constraint imposes fundamental limits to the system's stabilizability and tracking performance, which depend on the unstable poles and nonminimum phase zeros of the system. In particular, for MIMO systems, these limits are seen to be dependent on the directions of the unstable poles and nonminimum phase zeros. Moreover, we also show that to achieve the optimal tracking performance, the total channel power must be allocated to individual channels proportional to their degrees of difficulty to control, a scheme that departs fundamentally from the Shannon's classical 'water-filling' strategy.