Computation of control for linear approximately controllable system using weighted Tikhonov regularization

摘要

Computing steering control for an approximately controllable linear system for a given target state is an ill-posed problem. We use a weighted Tikhonov regularization method and compute the regularized control. It is proved that the target state corresponding to the regularized control is close to the actual state to be attained. We also obtained error estimates and convergence rates involved in the regularization procedure using both the a priori and a posteriori parameter choice rule. Theory is substantiated with numerical experiments.