Quantum Schrödinger equation, describing dynamical spin-interaction of two electrons with external magnetic field, is considered as an object for cybernetic research. Indeed, because of having a possibility to change external magnetic field, we can influence the interaction of particles. The algorithm of investigation of the algebraic structure of the spin-system is given. A specification of this algorithm is essentially connected with a control aspect. The spin-system is decomposed into six subsystems by us-ing the found algebraic structure. Five from them are one-dimensional noninteract subsystems. Every from the latter has his own one-dimensional control. 1 Description of the system Let us consider a Schrödinger equation for the spin-state X (t) of two spin-interacting electrons in an external inhomogeneous magnetic field [1] ih̄ d dt
We consider the problem of steering control for the systems of one spin 1/2 particle and two interacting spin 1/2 particles in an electromagnetic field. The describing models are bilinear systems whose state varies on the Lie group of special unitary matrices of dimensions two and four, respectively. For both systems, we describe their controllability properties and provide constructive control algorithms. The algorithms based on optimal control theory consider the time of transfer as cost functional. Explicit expressions are derived for the time optimal controls. The algorithms based on Lie group decompositions improve over previously presented algorithms in that they allow an explicit analytic calculation of the parameters involved which does not require any numerics.