Convergence of the costates does not imply convergence of the control

A study conducted that the convergence of the costates does not imply convergence of the control. The study focused on a problem that describes a particle of unit mass, moving in a linear resistive medium. The optimal control problem is to minimize the total amount of work done. The study demonstrated that it can be easily shown that the exact values of the costates are given by a direct application of the minimum principle. The study states that proper psedosectral (PS) method for solving a finite-horizon optimal control problem needs to be based on Gauss-Lobatto points. The counterexample described in the study also reveals that the convergence cannot be proved for PS methods, based on Gauss-Radau and Gauss points.