The Rate of Convergence for a Pseudospectral Optimal Control Method

Over the last decade, pseudospectral (PS) methods have emerged as a popular computational solution for the problem of nonlinear constrained optimal control. They have been applied to many industrial-strength problems, notably the recent zero-propellant-maneuvering of the International Space Station performed by NASA. In this paper, we prove a theorem on the rate of convergence for the approximate optimal cost computed using PS methods. This paper contains several essential differences from existing papers on PS optimal control as well as some other direct computational methods. First, the proofs do not use necessary conditions of optimal control. Secondly, we do not make coercivity type of assumptions. As a result, the theory does not require the local uniqueness of optimal solutions. The proof is not build on the bases of consistency approximation theory. Thus, we can remove some restrictive assumptions in the previous results on PS optimal control methods.