Non-causal iterative learning algorithm with variable forgetting factor

A non-causal iterative learning algorithm (ILC) with variable forgetting factor is proposed for a class of nonlinear system with initial error. This algorithm eliminates the limitation that the initial state should be consistent with the desired one or fixed in the learning process of conventional algorithms. The error information of future time in previous iteration is used to correct the control law in the non-causal ILC algorithm, so the controller has the function of compensating future disturbances ahead of time. The introduced variable forgetting can adjust the control input effectively and do filtering in the iteration direction, thus it accelerates the convergent speed and weakens the influence on the convergence which is generated from the indeterminacy. Compared with the conventional PD-type algorithm, this algorithm not only increases information content but also avoids using the derivative of error signals. From the perspective of execution, it is easier to measure, and the noise level is greatly reduced. At last, the new algorithm presented in the paper is used in the simulation test of manipulator trajectory tracking, and the result illustrates effectiveness and real-time performance.