Iterative learning control with fixed reference batch and exponential learning gain for linear systems

A new iterative learning control (ILC) method is presented for the trajectory tracking control of a kind of linear system. This new method does not need much detailed knowledge of the system. After a fixed reference batch is properly selected, the ratio of the input change and corresponding output change between the current and fixed reference batches multiplied by an exponential learning coefficient can be used as the learning gain in the ILC law in order to calculate the input of next batch. The method can track the desired trajectory successfully while the batch number goes on. The convergence of the proposed method is analyzed and proved. The proposed method is validated on linear time-invariant (LTI) and linear time-variant (LTV) systems.