Asymptotic solution of the optimal speed problem for the quasilinear system under Euclidean constraint on control

For the system with a small parameter under nonlinearities, consideration was given to the problem of optimal speed. The values of the multivariable control actions are bounded in the Euclidean norm. The theorem of existence and asymptotic properties of the solution of this problem was proved. It underlies the algorithm to construct asymptotic arbitrary-order approximations to the optimal control.