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Finite Difference Based Iterative Learning Control with Initial State Learning for Fractional Order Linear Systems

Yong-Hong Lan*, Bin Wu, and Yi-Ping Luo
International Journal of Control, Automation, and Systems, vol. 20, no. 2, pp.452-460, 2022

Abstract : This paper presents a PI-type iterative learning control (ILC) law with initial state learning for a class of α (0 < α ≤ 1) fractional order linear systems. First, by using backward difference method, the finite difference approximation of the fractional order derivative is obtained, which leads to globally 2−α order accuracy. Then, a PIILC law is constructed at the nodes and the convergence analysis of the iterative scheme is proved. A new sufficient condition is derived to guarantee that the tracking error is asymptotical convergent. The obtained convergence condition is fractional order dependent and is less conservative than the existing one. Most of the classical ILC conditions for fractional order linear systems fall into the special case of this paper. Finally, the simulation results show the effectiveness of the proposed control method.

Keyword : Finite difference, fractional order, initial state learning, iterative learning control, linear system.

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