This article proposes an accelerated learning control framework for point-to-point (P2P) tracking systems subject to stochastic noise, with a focus on reducing input energy. A novel stochastic accelerated method with a fixed penalty factor is established, resulting in substantial performance advancements for the overall iteration process. In this method, we introduce a two-loop structure. A historical term is designed and appropriately incorporated into the input update to improve the convergence process of the inner loop, and a Lagrange multiplier is updated in the outer loop to ensure the input sequence to converge to a limit that is closest to the initial input, achieving the effect of energy reduction. Additionally, practical implementation of the proposed framework is addressed by terminating the inner loop within a finite number of iterations according to a given accuracy. In this scenario, two types of Lagrange multiplier updating are conducted to handle the noise's impact. Numerical simulations are provided to validate the theoretical results.
Qian et al. (Thu,) studied this question.