Two-point boundary value problem of control systems with parameter

We consider the problem of optimum concerning to the minimization quadratic functionals of Bolza type with constraints represented differential systems with parameter. One demonstrates the uniqueness of optimal feedback nonlinear control obtained, by utilizing that the U Hilbert space control domain is rotund. The solution for two point boundary value problem implies the determination of the solution of the system in variations associated to the linearized system. The construction of the solution use of an iterative procedure, yielding the initial value results of the adjoint variable. By presenting the state vectors x ∈ X and the control vectors u ∈ U in orthonormal basis, one develops a numerical approximation method of the solution to the optimum problem.