Lebesgue-p Norm Convergence Analysis of PDα-Type Iterative Learning Control for Fractional-Order Nonlinear Systems
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 Gro...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/5157267 |
| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |