Dual convergence of the legendre pseudospectral method for solving nonlinear constrained optimal control problems

In this paper we present a modified Pseudospectral method for constrained nonlinear optimal control problems. The convergence is guaranteed under verifiable conditions. We also show that the convergence of the primal variables does not necessarily imply convergence of the duals. The Covector Mapping Theorem is clarified and the issue of constraint qualifications is demonstrated by a simple example. Conditions for the convergence of the duals are described and illustrated.