In this paper we obtain information theoretical conditions for tracking in linear time-invariant control systems. We consider the particular case where the closed loop contains a channel in the feedback loop. The mutual information rate between the feedback signal and the reference input signal is used to quantify information about the reference signal that is available for feedback. This mutual information rate must be maximized in order to improve the tracking performance. The mutual information is shown to be upper bounded by a quantity that depends on the unstable eigenvalues of the plant and on the channel capacity. If the channel capacity reaches a lower limit, the feedback signal becomes completely uncorrelated with the reference signal, rendering feedback useless. We also find a lower bound on the expected squared tracking error in terms of the entropy of a random reference signal. Examples and simulations are provided to demonstrate the results.
Decision and Control
channel capacity, closed loop systems, eigenvalues and eigenfunctions
Abdallah, Chaouki T.; I Lopez; S.K. Jayaweera; and H. Tanner. "Conditions for tracking in networked control systems." Decision and Control (2008): 3626-3632. https://digitalrepository.unm.edu/ece_fsp/77