The optimal control synthesis for quantum-mechanical system

It is consider the unbounded optimal control problem of oscillating system which represents the well-known Landau-Zener quantum mechanical model. This problem is degenerate and has a family of turnpike solutions, which can be constructed according to the theory by converting to the derived problem of lower order. This family specifies the synthesis of optimal control in the derived problem and then the approximate synthesis with any accuracy in the original problem.