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

Abstract EN

The first-order and second-order PDα-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 (Lp) 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 PDα-type ILC is investigated, while the convergence of the second-order PDα-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.