On control processes in the systems of counteracting spins

The model of quantum system of interacting spins based on Shr$\rm\ddot{o}$dinger equation with linear control is transformed to the derived system (known from the degenerate problems theory), equivalent to the original one, but regular and simmetric opens new perspectives of investigaton for different particular cases.
It is considered a typical case when control action is distributed uniformly to all spins. In this case the derived system proved to be same Shrödinger equation without control and regular description of impulse control modes at the boundaries of time interval. An effective algorithm of control optimization is proposed.