Convergence rates for direct transcription of optimal control problems with final-time equality constraints using collocation at Radau points

In this paper, we present convergence rates for the error between the direct transcription solution and the true solution of an optimal control problem with final-time equality constraints, as a function of the discretization size. The problem is discretized using collocation at Radau points. We analyze convergence from an NLP/matrix algebra perspective. The work also reveals the role of controllability in the convergence analysis. As an outcome, we have an adjoint estimation procedure derived from the Lagrange multipliers for the large scale NLP