Accelerating Iterative Learning Control Using Fractional-Proportional-Type Update Rule

Using the proportional-type update rule (PTUR) is the most common update approach for iterative learning control. By combining PTUR and a newly proposed fractional-power-type update rule (FTUR), a fractional-proportional-type update rule is proposed to achieve fast convergence for scenarios where the tracking errors can be large or small. The nonlinearity of fractional power term and tracking error accumulation along the time axis introduce considerable challenges in convergence analysis and convergence rate estimation. Thus, a novel analysis method is proposed for nonlinear recursion with perturbation where the convergence is established as per nonlinear tracking-error dynamics. The limits of the tracking errors are demonstrated independent of the system matrices. The relationship between the convergence limit and initial tracking error is examined. Moreover, the local and global convergence rates are provided. The proposed approach exhibits an advantage in terms of the convergence rate compared with PTUR and FTUR. Optimal parameter selection is achieved based on the convergence rate. The theoretical results are confirmed via numerical simulations.