Adaptive Gain Design for Learning Tracking Systems Over Fading Communication

ABSTRACT This paper investigates the adaptive gain design for discrete‐time stochastic systems with fading measurements, aiming to achieve fast transient convergence and high final tracking accuracy. The fading measurements introduce output‐dependent noise comprising both multiplicative and additive randomness, where the magnitude of the noise varies from iteration to iteration. The output‐dependent noise leads to challenges in gain design and learning‐tracking control. We propose a noise‐adaptive learning control (NALC) algorithm with adaptive decreasing gain. Relying on observed output error information, the adaptive gain dynamically adjusts its rate of decrease in response to output‐dependent noise. When the output‐dependent noise is significant, the adaptive decreasing gain decreases rapidly to mitigate the impact of the noise; otherwise, the adaptive decreasing gain remains constant or decreases slowly to accelerate the reduction of tracking errors. The input error is proved to converge to zero in the almost sure sense. The example of a permanent magnet synchronous motor is provided to verify the proposed algorithm.