Iterative learning algorithms for boundary tracing problems of nonlinear fractional diffusion equations

In this paper, the iterative learning control technique is extended to distributed parameter systems governed by nonlinear fractional diffusion equations. Based on $P$-type and $P{I}^{\theta }$-type iterative learning control methods, sufficient conditions for the convergences of systems are given. Finally, numerical examples are presented to illustrate the efficiency of the proposed iterative schemes. The numerical results show that the closed-loop iterative learning control scheme converges faster than the open-loop iterative learning control scheme and the $P{I}^{\theta }$-type iterative learning control scheme converges faster than the $P$-type and the $PI$-type iterative learning control scheme.