For the discrete linear multi-agent systems with random actuator faults and system disturbances, an iterative learning control strategy with the forgetting factor is proposed. Firstly, the random variation of actuator faults with the number of iterations is considered. A multiplicative stochastic fault model obeying a normal distribution is designed, and the correction mechanism is given. Secondly, an iterative learning consistency control algorithm with a forgetting factor is provided under the consideration of random disturbances in the system. The system stability is analyzed by using the mean square stability theory. A sufficient condition for the consistency in the multi-agent system is given through the relevant mathematical derivation, which makes it possible to realize the state consistency for the discrete multi-agent system under the occurrence of random faults in the actuator. Finally, the feasibility of the algorithm is verified by numerical simulation in a multi-agent system.
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