Costate computation by a Chebyshev pseudospectral method

Abstract

Among the various pseudospectral (PS) methods for optimal control [1], only the Legendre PS method has been mathematically proven to guarantee the feasibility, consistency, and convergence of the approximations [2–5]. As exemplified by its experimental and flight applications in national programs [6–10], it is not surprising that the Legendre PS method has become the method of choice [11–19] in both industry and academia for solving optimal control problems. Efforts to improve the Legendre PS methods by using either other polynomials [20–22] or point distributions [23,24] have not yet resulted in any rigorous framework for convergence of these approximations [24,25].