Singular Distributed Parameter System Iterative Learning Control with Forgetting Factor with Time- Delay

In this paper, an iterative learning control topic for a kind of singular distributed parameter system with forgetting with time-delay which initial value can vary in a little space has been discussed. And a high level algorithm is extended and proven, using Green formula and Gronwall inequality, that it is suitable for the given system. Convergence of the proposed approach is analyzed and the uniform boundedness of tracking error is obtained in this paper. Numerical simulation is presented for a parabolic partial differential equations solved using ILC based on Eular difference format. At present, the application research of ILC method to the singular distributed parameter system with forgetting factor with time-delay is less. So this paper expands the scope of research for singular system and iterative learning control. Numerical example is given to illustrate the effectiveness of the proposed method.