Iteration Number Bound for Adaptive Learning Control of Nonlinear Systems Under Specified Approximation Error

This study addresses the tracking problem for a class of nonlinear uncertain systems over a finite time interval, where the unknown and nonparametric nature of the system's nonlinear functions is taken into consideration. In the context of adaptive iterative learning control, it becomes necessary to employ known basis functions in order to approximate the nonlinear uncertainty for parameterizations. These basis functions must be sufficient to ensure convergence of tracking error. The relationship between the number of bases used and the iteration count plays a significant role in achieving desired tracking accuracy. Additionally, when applying adaptive iterative learning control, resetting the initial state of the system introduces uncertainty in terms of initial state error, which affects the iteration count. In this study, we examine five different conditions related to initial state error and establish an upper bound on iterations that is proportional to approximation error under these conditions. Our analysis provides valuable insights for accelerating convergence rate.