Iterative learning algorithms for boundary tracing of fractional diffusion equations

We study P-type and PI ${}^{\theta }$-type iterative learning control (ILC) schemes for boundary tracing problem of nonhomogeneous fractional diffusion equations. Based on Sobolev imbedding theorem, we derive sufficient conditions for the convergence of four ILC schemes in the sense of $\lambda$-norm. Numerical examples are presented to illustrate effectiveness of the proposed control methods. The results show that closed-loop ILC scheme converges faster than open-loop ILC scheme; moreover, PI ${}^{\theta }$-type $(0.5<\theta <1)$ ILC scheme outperforms P-type and PI-type $(\theta =1)$ ILC schemes in terms of the convergence speed.