Covector Estimation for Optimal Control Solver Using a Jacobi Pseudospectral Method

Abstract

This paper presents a Jacobi-pseudospectral (PS) method for directly estimating covectors of the optimal control problem. The covector mapping theorem (CMT) denotes connection between covectors of the minimum-principle and the Karush-Kuhn-Tucker (KKT) multipliers. The CMT for both the Legendre-PS method and the Chebyshev-PS method are proved already. However, applicability of the Jacobi-PS method which including these specific orthogonal polynomial methods has not been studied. The proposed method shows that by applying the weighted interpolants, the Jacobi-PS with the weights of high-order Gauss-Lobatto formulae also satisfy the CMT. Hence, the direct solution by this method automatically yields the covectors by way of the KKT multipliers that can be extracted from a nonlinear programming problem solver. Numerical examples demonstrate that this method yields accurate results compare to the indirect method.