Enhanced-Input Learning Control: Toward Novel Historical Information Reusing in Stochastic Iterative Learning Control

This study investigates a novel iterative learning control scheme for stochastic systems that effectively utilizes historical information. In this approach, an additional historical input term is incorporated, and an adjustable decreasing sequence of learning gains is introduced to the conventional proportional-type learning control scheme. Unlike relying solely on the input signal generated by the previous iteration, this approach leverages the historical input information without resorting to an averaging strategy, which is common in existing high-order learning control schemes. The convergence is rigorously demonstrated within a stochastic framework. Furthermore, the asymptotic convergence rate of both the proposed learning control scheme and the conventional proportional-type scheme are characterized. Building upon this foundation, it is further illustrated that applying appropriate learning gains in the new scheme can enhance its convergence rate significantly. Numerical simulations are conducted to validate the theoretical findings.