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.

scholarly journals PDα-type iterative learning control with initial state learning for fractional-order systems

2021 ◽  
Vol 39 (2) ◽  
pp. 400-406
Author(s):  
Fen Liu ◽  
Kejun Zhang
Keyword(s):  
Fractional Order ◽  
Iterative Learning Control ◽  
Tracking Error ◽  
Sufficient Conditions ◽  
Learning Control ◽  
Young Inequality ◽  
Iterative Learning ◽  
Initial State ◽  
Arbitrary Initial State ◽  
State Learning

In order to eliminate the influence of the arbitrary initial state on the systems, open-loop and open-close-loop PDα-type fractional-order iterative learning control (FOILC) algorithms with initial state learning are proposed for a class of fractional-order linear continuous-time systems with an arbitrary initial state. In the sense of Lebesgue-p norm, the sufficient conditions for the convergence of PDα-type algorithms are disturbed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral. The results demonstrate that under these novel algorithms, the convergences of the tracking error are can be guaranteed. Numerical simulations support the effectiveness and correctness of the proposed algorithms.

Sign in / Sign up

Export Citation Format

Share Document