Reconstruction of controls and parameters by the Tikhonov method with non-smooth stabilizers

We consider the problem of the reconstruction of an a priori unknown control in a dynamic system based on approximate a posteriori observations of the motion of this system. We propose to solve this problem by the Tikhonov method with a stabilizer which contains the total variation of the control. This provides the piecewise uniform convergence of regularized approximations and thus enables one to numerically reconstruct the fine structure of the desired solution.