On the Pseudospectral Covector Mapping Theorem for Nonlinear Optimal Control

In recent years, a large number of nonlinear optimal control problems have been solved by pseudospectral (PS) methods. In an effort to better understand the PS approach to solving control problems, we present convergence results for problems with mixed state and control constraints. A set of sufficient conditions are proved under which the solution of the discretized optimal control problem converges to the continuous solution. Conditions for the convergence of the duals are described and illustrated. This leads to a clarification of covector mapping theorem and its connections to constraint qualifications