For non-Gaussian stochastic distribution systems with faults and disturbances, a novel robust fault-tolerant control scheme is proposed based on Iterative Learning Observer (ILO).The linear B-spline neural network is used to establish the relationship between output Probability Density Function (PDF) and dynamic weights.An iterative learning observer is designed to accurately estimate the faults with less computational load.By using the fault estimation information, a fault-tolerant controller is designed, so that the system can still track the expected weight vector after the fault occurs.Simulation results demonstrate the effectiveness of the proposed approach.The iterative learning observer can rapidly reconstruct the faults after a short transition period, and the fault-tolerant controller based on PI tracking has good tracking effects on both the constant and time-varying weight vectors.