High-Order \(\mathcal{D}^{\alpha}\)-Type Iterative Learning Control for Fractional-Order Nonlinear Time-Delay Systems
This paper presents a high-order \(\mathcal{D}^{\alpha}\)-type iterative learning control (ILC) scheme for a class of fractional-order nonlinear time-delay systems. First, a discrete system for \(\mathcal{D}^{\alpha}\)-type ILC is established by analyzing the control and learning processes, and the ILC design problem is then converted to a stabilization problem for this discrete system. Next, by introducing a suitable norm and using a generalized GronwallBellman Lemma, the sufficiency condition for the robust convergence with respect to the bounded external disturbance of the control input and the tracking errors is obtained. Finally, the validity of the method is verified by a numerical example.
iterative learning control fractional-order nonlinear time-delay system generalized gronwallbellman lemma