Barrier Lyapunov function-based fuzzy adaptive iterative learning control

In this paper, the problem of error-constrained adaptive iterative learning control is presented for a class of nonlinear systems which performs a given task over a finite time interval repeatedly, where the fuzzy system is used to approximate the unknown nonlinearity. Different from the output tracking control, the error tracking approach is used to deal with arbitrary initial conditions. An improved logarithmic barrier Lyapunov function is given to design an adaptive iterative learning controller, by applying the error tracking approach. It is shown that the practical tracking error trajectory is ensured to converge to the desired error trajectory as the iteration increases, and kept in the pre-specified region all the time. An illustrative example is presented to demonstrate the effectiveness of the proposed method.