Convergence analysis of PDα type iterative learning control for a class of fractional-order nonlinear systems

Abstract

Abstract: For a class of single input and single output (SISO) fractional-order nonlinear continuous systems, by taking advantage of the generalized Young inequality of convolution integral, the sufficient conditions for the convergence of open-loop, closed-loop and open-closed-loop PD^α type fractional-order iterative learning control (FOILC) algorithms are presented in the sense of L^p norm with strict theoretical proof of these algorithms followed. It is found that the sufficient conditions for the convergence of the control algorithms depend on the gains of the algorithms and the attributes of the systems themselves. The open-closed-loop PD^α-type control algorithm has faster convergence speed than the open-loop control algorithm under appropriate gain matrices. These conclusions are the same as those of fractional-order linear systems. The simulation experiments further verify the feasibility and the correctness of the above theory.

Key words: fractional-order, iterative learning control, L^p norm, convergence

CLC Number:

TP13

ZHANG Ke-jun, PENG Guo-hua, DU Yong-jun. Convergence analysis of PD^α type iterative learning control for a class of fractional-order nonlinear systems[J]. Journal of Lanzhou University of Technology, 2022, 48(5): 92-98.

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Convergence analysis of PD^α type iterative learning control for a class of fractional-order nonlinear systems

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