Stochastic iterative learning control of continuous linear system

In this paper, iterative learning control is applied to the continuous linear time invariant system with random noise term. The system with continuous time and discrete iteration number is thought as the hybrid system, which becomes more complex than exists systems based on iterative learning control. It is proved that the input error and tracking error along the iteration direction can converge to be bounded in the mean square sense using Gronwall inequality and stochastic differential equation theory. The results show that tracking error have closely relation with noise covariance. Finally, the effectiveness of the algorithm is verified by numerical simulation.