Iterative learning control for nonlinear systems using global Newton and secant learning schemes

Abstract This paper proposes a global Newton‐type and a global secant‐type learning schemes for nonlinear systems. The aim of the study is to use the learning schemes to prove that the output trajectory can converge to the desired trajectory along the iteration axis. Our main idea is to divide the distance between the desired trajectory and the initial trajectory into several segments, so that each segment satisfies the conditions of Newton‐type and secant‐type learning algorithms, and then construct a contraction mapping of the tracking error for each segment ensure that the output trajectory converges along the iteration axis. In addition, the convergence speed of the secant‐type learning algorithm is evaluated by a ‐factor and compared with the convergence speed of the ‐type learning scheme. Finally, we numerically simulate the switched reluctance motor system to verify the effectiveness of the proposed algorithms.