Practical Learning-Tracking Framework Under Unknown Nonrepetitive Channel Randomness

Abstract

In this study, we consider the learning-tracking problem for stochastic systems through unreliable communication channels. The channels suffer from both multiplicative and additive randomness subject to unknown probability distributions. The statistics of this randomness, such as mean and covariance, are nonrepetitive in the iteration domain. This nonrepetitive randomness introduces non-stationary contamination and drifts to the actual signals, yielding essential challenges in signal processing and learning control. Therefore, we propose a practical framework constituted by an unbiased estimator of the mean inverse, a signal correction mechanism, and learning control schemes. The convergence and tracking performance are strictly established for both constant and decreasing step-lengths. If the statistics satisfy asymptotic repetitiveness in the iteration domain, a consistent estimator applies to the framework while retaining the framework’s asymptotic properties. Illustrative examples are provided to verify the theoretical results.