Fractional-order iterative learning control with initial state learning design

In this paper, we present a fractional-order iterative learning control (ILC) framework with initial state learning for the tracking problems of linear time-varying systems. Both open-loop and closed-loop $D^{\alpha }$-type iterative learning updating laws are considered. To design ILC scheme for practical control systems, initialization assumption, i.e., the system initial states should be the same at each repetition, is removed by using an initial state learning scheme together with the $D^{\alpha }$-type ILC updating law. Sufficient conditions of convergence to the desired trajectory is theoretically proved for a linear time-varying mechanical system. Numerical simulation results are presented to illustrate effectiveness of the control strategies. Moreover, we also show that the proposed learning scheme can be applied to the motion control of robot manipulators under some reasonable conditions.