Lebesgue-\(p\) norm convergence analysis of PD\(^\alpha\)-type iterative learning control for fractional-order nonlinear systems
Summary: The first-order and second-order PD\(^\alpha\)-type iterative learning control (ILC) schemes are considered for a class of Caputo-type fractional-order nonlinear systems. Due to the imperfection of the \(\lambda\)-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-type ILC is investigated, while the convergence of the second-order PD-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.
scientific article; zbMATH DE number 7026604