On the controllability of some closed finite-dimensional systems with control in energy levels

The analysis of controllability in systems with different types of control actions is one of the essential problems in quantum control theory. Before synthesizing specific controls or studying the properties of objective functions, it is necessary to verify that the system under consideration allows for the required evolution using the available means of influencing its dynamics. This presentation is devoted to ongoing work on the analysis of complete controllability for systems of a special type, namely, certain classes of systems with control in the energy levels. It will be shown that the addition of such control can expand the possibilities for manipulating the state of the system. Some general results on the controllability of closed finite-dimensional systems with control in the energy levels will be presented, as well as controllability conditions for a number of small-dimensional systems.