Adaptive iterative feedback control for nonlinear system with unknown high-frequency gain

An adaptive iterative feedback control approach is proposed for a class of single-input, single-output uncertain nonlinear systems with completely unknown high-frequency feedback gain. Unlike the common iterative learning control that requires some preconditions of stability on the learning gain, the adaptive iterative feedback control obtains the convergence through the change of high-frequency feedback gain in a Nussbaum-type function. This paper shows the repetitive tracking error sequence is asymptotic to zero when the iterative sequence i → ∞. Simulation is presented to show the validity of the proposed control method.