An Accelerated Adaptive Gain Design in Stochastic Learning Control

This study investigates the trajectory tracking problem for stochastic systems and proposes a novel adaptive gain design to enhance the transient convergence performance of the learning control scheme. Differing from the existing results that mainly focused on gain's transition from constant to decreasing ones to suppress noise influence, this study leverages the adaptive mechanisms based on noisy signals to achieve an acceleration capability by addressing diverse performance at different time instants throughout the operation interval. Specifically, an additional gain matrix is introduced into the adaptive gain design to further enhance transient convergence performance. An iterative learning control approach with such a gain design is proposed to realize high precision tracking and it is proven that the input error generated by the newly proposed learning control scheme converges almost surely to zero. The effectiveness of the proposed scheme and its improvement on the transient performance of the learning process are numerically validated.