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In order to eliminate the influence of the arbitrary initial state on the systems, open-loop and open-close-loop PD  α  -type fractional-order iterative learning control (FOILC) algorithms with initial state learning are proposed for a class of fractional-order linear continuous-time systems with an arbitrary initial state. In the sense of Lebesgue- p  norm, the sufficient conditions for the convergence of PD  α  -type algorithms are disturbed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral. The results demonstrate that under these novel algorithms, the convergences of the tracking error are can be guaranteed. Numerical simulations support the effectiveness and correctness of the proposed algorithms.

PDα-type iterative learning control with initial state learning for fractional-order systems

PD^α-type iterative learning control with initial state learning for fractional-order systems