Performance-driven selective high-order stochastic iterative learning control with probabilistic guarantees

This paper investigates stochastic iterative learning control (SILC) for discrete-time linear time-varying systems subject to process and measurement noise. High-order learning can smooth input updates by reusing historical errors, but a fixed high-order structure may sacrifice transient tracking performance when obsolete or poorly aligned data are incorporated. To address this smoothing-transient trade-off, we develop a selective enhanced high-order SILC, in which historical tracking errors are treated as candidate learning data and are admitted only through a performance-driven probabilistic test. Historical information is used only when its predictive surrogate outperforms the proportional-type baseline with a prescribed conditional probability under an auxiliary law or moment class. We establish directional and feasibility results, ideal and practical surrogate guarantees, variance reduction, and asymptotic convergence. Furthermore, the asymptotic convergence of the proposed method is proved. The simulation results illustrate the effectiveness of the proposed selective high-order learning strategy in improving the transient-smoothness trade-off.