On a connection of the approximation of nonlinear systems in the sense of time optimality and their algebraic approximation

The question of a connection of the asymptotic behavior of a solution of the time-optimal control problem and properties of the algebra of nonlinear power moments is considered. Namely, it is shown that if a certain moment min-problem approximates the time-optimal control problem then under certain additional assumptions the structures generated in the algebra by this moment problem and by the nonlinear system coincide.