The parameterization method in optimal control problems and differential–algebraic equations

The paper is devoted to the explanation of the numerical parameterization method (PM) for optimal control (OC) problems with intermediate phase constraint and to its circumstantiation for classical calculus of variation (CV) problems that arise in connection with singular ODEs or DAEs, especially in cases of their essential degeneracy. The PM is based on a finite parameterization of control functions and on derivation of the problem functional with respect to control parameters. The first and the second derivatives are calculated with the help of adjoint vector and matrix impulses. Results of the solution to one phase constrained OC and two degenerate CV problems, connected with singular DAEs nonreducible to the normal form, are presented.