Non-uniform trajectory tracking adaptive iterative learning control for nonlinear pure-feedback systems with initial state error based on RBF-neural network

An adaptive iterative learning control strategy is presented for a class of nonlinear pure-feedback systems with initial state error using RBF-neural network to solve the problem of non-uniform trajectory tracking. The proposed control scheme utilizes RBF-neural network to learn the behavior of the unknown plant dynamics. Filtered signals are employed to circumvent algebraic loop problems encountered in the implementation of the existing controllers. Backstepping design technique is applied to deal with system dynamics. Based on the Lyapunov-like synthesis, we show that all signals in the closed-loop system remain bounded over a pre-specified time interval [0, T ]. There even exist initial state errors, the norm of tracking error vector will asymptotically converge to a tunable residual set as iteration goes to infinity. A time-varying boundary layer is introduced to solve the problem of initial state error. A typical series is introduced in order to deal with the unknown bound of the approximation errors and complete the non-uniform trajectory tracking problem. Finally, the simulation example of one-link robot system shows the feasibility and effectiveness of the approach.