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The first-order and second-order PD  α  -type iterative learning control (ILC) schemes are considered for a class of Caputo-type fractional-order nonlinear systems. Due to the imperfection of the    λ   -norm, the Lebesgue- p  (L    p) norm is adopted to overcome the disadvantage. First, a generalization of the Gronwall integral inequality with singularity is established. Next, according to the reached generalized Gronwall integral inequality and the generalized Young inequality, the monotonic convergence of the first-order PD  α  -type ILC is investigated, while the convergence of the second-order PD  α  -type ILC is analyzed. The resultant condition shows that both the learning gains and the system dynamics affect the convergence. Finally, numerical simulations are exploited to verify the results.

Lebesgue-p Norm Convergence Analysis of PDα-Type Iterative Learning Control for Fractional-Order Nonlinear Systems

Lebesgue-p Norm Convergence Analysis of PD^α-Type Iterative Learning Control for Fractional-Order Nonlinear Systems