Projection methods for improving controls in nonlinear control systems with terminal constraints

In this paper, we consider a new approach to the optimization of nonlinear control systems with terminal constraints based on the consecutive solution of nonlocal control improvement problems in the form of special systems of functional equations in the control space. The corresponding systems are constructed as fixed-point problems for special control operators with an additional algebraic equation. The methods of successive approximations of the control that preserve terminal constraints at each iteration used in this paper do not contain the time-consuming operation of parametric variation of the control, which is typical for common gradient methods.