Neural AILC for Error Tracking Against Arbitrary Initial Shifts

This paper concerns with the adaptive iterative learning control using neural networks for systems performing repetitive tasks over a finite time interval. Two standing issues of such iterative learning control processes are addressed: one is the initial condition problem and the other is that related to the approximation error. Instead of the state tracking, an error tracking approach is proposed to tackle the problem arising from arbitrary initial shifts. The desired error trajectory is prespecified at the design stage, suitable to different tracking tasks. The initial value of the desired error trajectory for each cycle is required to be the same as that of the actual error trajectory. It is just a requirement for the initial value of the desired error trajectory, but does not pose any requirement for the initial value of the actual error trajectory. It is shown that the actual error trajectory is adjustable and is able to converge to a prespecified neighborhood of the origin, while all variables of the closed-loop system are of uniform boundedness. The robustness improvement in case of nonzero approximation error is made possible due to the use of a deadzone modified Lyapunov functional. The resultant estimation for the bound of the approximation error avoids deterioration in tracking performance. The effectiveness of the designed learning controller is validated through an illustrative example.