Perturbed inverse reconstruction problems for controlled dynamic systems are under consideration. A sample history of the actual trajectory is known. This trajectory is generated by a control, which isn’t known. Moreover, the deviation of the samples from the actual trajectory satisfies the known estimate of the sample error. The inverse problem with perturbed (inaccurate) sample of trajectory consists of reconstructing trajectories which are close to the actual trajectory in C. Controls generating the trajectories should be close in $$L_{2}$$ to the normal control generating the actual trajectory and have the least norm in $$L_{2}$$. A numerical method for solving this problem is suggested. The application of the suggested method is illustrated by the graphics.