Iterative learning control for nonlinear time-delay repetitive systems with arbitrary initial value

For a class of nonlinear time-delay repetitive systems with initial deviation, output error, disturbances and arbitrary initial value conditions, the PD type closed-loop iterative learning tracking control problem which satisfies the global Lipschitz conditions is investigated. By defining the bounded desired trajectory, expected control and the tracking error of the iterative learning process, the necessary and sufficient conditions for the existence of the gain of the learning controller is given through the λ norm theory and Bellman-Gronwall inequality, which can guarantee the tracking error of the closed-loop system to be bounded, and the uniform convergence criteria of the control algorithm are also proved. Simulation of the speed control of the injection molding machine demonstrate the proposed method of this paper not only can improve the performance of the system significantly, but also has certain inhibition effect on the bounded disturbance and arbitrary initial problem.