Accelerated Energy-Saving Learning Control for Stochastic Point-to-Point Tracking Systems

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.