Tracking error analysis of iterative learning control with exponential learning gain

An iterative learning control (ILC) with exponential learning gain based on a fixed reference batch is presented for the trajectory tracking control of a kind of linear system. A reference batch should be properly selected at first. Then the learning gain in the ILC law is the ratio of the input and output changes between the current batch and reference batch, multiplied by an exponential learning coefficient. Using the method, the desired trajectory can be tracked successfully while the batch number goes on. The asymptotic convergence of tracking error is analyzed, and sufficient condition to guarantee the monotonic convergence of the tracking error norm is also derived. The proposed method is validated on a linear time-invariant system.