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

Lei Li

Discrete Dynamics in Nature and Society, 2018, vol. 2018, 1-10

Abstract:

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 -norm, the Lebesgue- 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:5157267

DOI: 10.1155/2018/5157267

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