Neural network-based AILC for non-repetitive trajectory tracking of non-affine pure-feedback discrete-time systems

Abstract

In this paper, a neural network-based adaptive iteration learning control (AILC) scheme is constructed for a class of non-affine pure-feedback discrete-time systems, which can fulfill the non-repetitive trajectory tracking tasks under random iterative initial errors. Considering that the nonlinear dynamical system is with a non-affine pure-feedback structure, we first transform the system into a predictor form. Then, the desired control signal is achieved by implicit function theorem. A neural network with an adaptation law of the weight vector norm, rather than the weight vector itself, is utilized to approximate the obtained desired control signal iteratively. By using Lyapunov analysis, it is proven that all the system signals are bounded and the system tracking error converges to a neighborhood around zero as iteration number goes to infinity. In contrast to the existing neural network-based AILC results, the most advantage of the proposed neural network-based AILC is that the number of the adjustable parameters is highly reduced. The effectiveness of the algorithm is verified by a simulation example.