Problem of optimal stabilization under integrally small perturbations

In the present work the optimal stabilization problem of a moving mass center of satellite under influence of integrally small perturbations during finite time intervals has been considered. The optimal stabilization problem of the above motion in classical sense and under integrally small perturbations is assumed and respectively solved. A comparison between the optimal values of performance indices in mentioned cases proves that the energy consumption at stabilization under integrally small perturbations is less than stabilization in classical sense.