ヤコビ擬スペクトル法を用いた最適制御問題の解法における双対変数の推定

抄録

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.