Iterative learning control for nonlinear distributed parameter system with state time delay

The iterative learning control method is applied to distributed parameter systems governed by parabolic partial differential equations (PDE). In this paper, an iterative learning control topic for a kind of nonlinear distributed parameter system which initial value can vary in a little space has been discussed. And an high level algorithm is extended and proven, using Green formula and Gronwall inequality, that it is suitable for the given system. Numerical simulation is presented for a parabolic PDE solved using ILC based on Eular difference format. The numerical example is given to illustrate the effectiveness of the proposed method.