On one approach to optimization of nonlinear control systems with constraints

For a class of nonlinear optimal control problems with constraints, the problem of improving the admissible control is considered. The conditions for improving control in the considered class of problems are presented as a special system of functional equations in the control space, which can be interpreted as a fixed point problem. An iterative method is constructed to solve the fixed point problem. The proposed method of successive approximations with conservation of constraints at each iteration does not use the labor-intensive operation of parametric control variation, which is typical for gradient methods.