Iterative Learning Control Technique for Approximate Controllability of Hilfer Fractional Differential Systems With Impulsive Effects

This paper examines a new class of Hilfer fractional differential systems under the influence of non‐instantaneous impulses. First, we established the approximate controllability results for the considered problem by utilizing the fixed‐point method. Moreover, we derived a sequence of control functions by employing the iterative learning control updating law, which aimed to identify a desired control function to ensure that the error between the actual output and the desired reference trajectories converges to zero in a suitable norm, achieving uniform convergence. Consequently, the limit of the sequence of control functions serves as the required control, ensuring that the problem is approximately controllable. Finally, an illustrative numerical example is given to demonstrate the obtained results.