高次ガウス・ロバット則の重み関数を用いたヤコビ擬スペクトル法による軌道最適化

抄録

This paper presents a Jacobi-pseudospectral method with the weights of high-order gauss-lobatto formulae for nonlinear optimal control problem. This method employs Nth-degree Jacobi polynomial approximations for the state and control variables with the values of these variables at the Jacobi-Gauss-Lobatto (JGL) points as the expansion coefficients. The performance index may be approximated using the high-order gauss-lobatto formulae. The weights from this approximation is expressible explicitly in terms of the Jacobi polynomial. This process yields a nonlinear programming problem (NLP) with the state and control values at the JGL points as unknown NLP parameters. Numerical examples demonstrate that this method yields accurate results compare to analytic solutions.