The problem of reconstructing unknown controls in hyperbolic systems from the results of approximate observations of motions of these systems is considered. To solve the problem, Tikhonov's method with a stabilizer containing the total time variation of the control is used. The use of such nondifferentiable stabilizer allows us to obtain more precise results in some cases than the approximation of the desired control in Lebesgue spaces. In particular, this method provides the piecewise uniform convergence of regularized approximations and makes possible the numerical reconstruction of the subtle structure of the desired control. © 2011 Pleiades Publishing, Ltd.