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Based on Nesterov accelerated gradient method, the problem of iterative learning control for a class of linear discrete-time systems is considered in this paper. Firstly, the iterative learning control problem of linear discrete-time systems is transformed into an iterative least-squares problem. Then, the Nesterov accelerated gradient method is introduced into the iterative learning control framework. Note that the Nesterov accelerated gradient learning algorithm has the capability of fast convergence. It is shown that the algorithm presented in this paper can guarantee the output tracking error converges to zero with rate <inline-formula> <tex-math notation="LaTeX">$O(1/k)$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> is the iteration counter. Moreover, the monotonic convergence of the Nesterov accelerated gradient learning algorithm is analyzed and discussed. Finally, the effectiveness of the proposed method is verified by two simulation examples.

Iterative Learning Control Based on Nesterov Accelerated Gradient Method