Compound FAT-based Learning Control of Uncertain Fractional-Order Nonlinear Systems With Disturbance

2021 ◽  
pp. 1-1
Author(s):  
Seyed Mehdi Abedi Pahnehkolaei ◽  
Javad Keighobadi ◽  
Alireza Alfi ◽  
Hamidreza Modares
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
Learning Control

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

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Lei Li
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
Integral Inequality ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Young Inequality ◽  
Second Order ◽  
Iterative Learning ◽  
First Order ◽  
Gronwall Integral Inequality

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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