Modification of the method of projections for improving the nonlinear controls

A method for the nonlocal improvement of controls in nonlinear systems based on the operation of projection onto the set of admissible control values. The peculiarity of the method is the possibility of nonlocal improvement of nonlinear control and control, satisfying the maximum principle. a new necessary condition for optimality that complement and reinforce the principle of differential peak-passer in the considered class of problems is received on the base of this method. An illustrative example of strict improvement of special management is given.