Iterative Learning Control for Linear Systems Subject to Random Disturbance: An Impulsive Approach

This paper investigates the tracking control problem of linear systems with random disturbances. Distinguishing itself from previous studies, this work models instantaneous external disturbances as impulse effects and employs a Bernoulli random variable to characterize their stochastic occurrence. After this, a random impulsive differential system is established and used for theoretical analysis. Based on this model, two iterative learning control strategies are applied to achieve the robust tracking. The theoretical results demonstrate that the proposed algorithms are successful in reducing the impact caused by random disturbances, enabling the system to perform robust tracking. Finally, a numerical simulation is provided to verify the effectiveness of the proposed approach.