Analysis of nonlinear discrete-time systems with higher-order iterative learning control

In this paper, an iterative learning control method is proposed for a class of nonlinear discrete-time systems with well-defined relative degree, which uses the output data from several previous operation cycles to enhance tracking performance. A new analysis approach is developed, by which the iterative learning control is shown to guarantee the convergence of the output trajectory to the desired one within bound and the bound is proportional to the bound on resetting errors. It is further proved effective to overcome initial shifts and the resultant output trajectory can be assessed as iteration increases. Numerical simulation is carried out to verify the theoretical results and exhibits that the proposed updating law possesses good transient behavior of learning process so that the convergence speed is improved.