Accelerated Iterative Learning Control Using Fractional High-Order Update Rule for LTI Systems

This study proposes an accelerated iterative learning control scheme using a fractional high-order update rule (FHUR) to improve the convergence rate for linear time-invariant systems. High- and low-order power update terms are used to handle large- and small-tracking errors, respectively, thereby accelerating convergence. Two learning mechanisms are proposed and shown to be optimal among various learning gain selections. The inherent nonlinearity in the FHUR poses significant challenges for the convergence analysis. To address this, a disturbed composite nonlinear mapping method is introduced. Using this method, the tracking errors are proven to converge either to an invariant set or to a set of limit cycles, depending on the underlying learning mechanism. Any desired tracking precision can be achieved by adjusting the parameters in the FHUR. Numerical simulations confirm that the FHUR presents a promising alternative to the commonly used proportional-type update rule for achieving accelerated convergence.