Development and experience of using the parameterization method in singular problems of dynamic optimization

The development and computational experience of the parameterization method for nonlinear problems of optimal control and classical calculus of variations are presented. The method consists in a finite-dimensional parameterization of admissible controls and the computation of derivative functionals of the problem with respect to the parameters with the help of adjoint systems. The convergence of the method with the growth of the complexity of the parameterized class is justified. Some results of the solution of a number of problems of optimal control and calculus of variations connected with the solution of differential-algebraic equations, in particular, with variable degeneration of Jacobian of the system are given.