In this article, a new learning-based time-varying impedance controller is proposed and tested to facilitate an autonomous physical human-robot interaction (pHRI). Novel adaptation laws are formulated for online adjustment of robot impedance based on human behavior. Two other sets of update rules are defined for intelligent coping with the robot's structured and unstructured uncertainties. These rules ensure stability via Lyapunov's theorem and provide uniform ultimate boundedness (UUB) of the closed-loop system's response, without a need for HRI force/torque measurement. Accordingly, the convergence of response signals, including errors in tracking, online impedance learning, robot parameter adaptation, and controller gain variation, is proven to operate in a bounded region (compact set) in the presence of robot and human uncertainties and bounded disturbances. The performance of the developed intelligent impedance-varying control strategy is investigated through comprehensive experimental studies in a repetitive following task with a moving target.