Control computation and error analysis for fractional evolution systems using Tikhonov regularization

Computing the control for controllable systems, particularly for approximately controllable systems, is interesting and challenging. This article focuses on the computation of control for an approximately controllable linear fractional diffusion system by converting the considered control problem into an equivalent ill-posed problem using operator theoretic formulations. We then solve the converted ill-posed operator equation for its regularized solution corresponding to the desired final state using the Tikhonov regularization technique. The selection of the regularization parameter ensures the convergence of the computed control. Finally, we exemplify the methodology numerically for two different target functions and plot the error graphs along with the truncated regularized control graphs using MATHEMATICA.