Closed-loop P-type iterative learning control of uncertain linear distributed parameter systems

An iterative learning control problem for a class of uncertain linear parabolic distributed parameter systems is discussed, which covers many processes such as heat and mass transfer, convection diffusion and transport. Under condition of allowing system state initially to have error in the iterative process a closed-loop P-type iterative learning algorithm is presented, and the sufficient condition of tracking error convergence in L² norm is given. Next, the convergence of the tracking error in L² and W^1,2 space is proved by using Gronwall-Bellman inequality and Sobolev inequality. In the end, a numerical example is given to illustrate the effectiveness of the proposed method.