A Technical Note on Convergence Analysis of AILC for a Class of Strict Feedback Nonlinear Systems

In the framework of iterative learning control (ILC), the evolution of the system along the iteration axis and the time axis are relatively independent. Confusing this independence may lead to imprecise mathematical derivations. In this paper, we point out that even if the extended error generated by the tracking error through a stable differential operator polynomial converges to zero in the iteration domain, it does not mean that the tracking error itself converges to zero. This issue is widely misused in the current adaptive ILC (AILC) design for strict feedback nonlinear systems. However, if the extended error can be guaranteed to converge to zero uniformly, the uniform convergence of the tracking error can be deduced. Utilizing this result, we correct the current AILC design and make it complete in mathematics.