High Accuracy Calculation of GaussWeights for Optimization Method by a Jacobi Pseudospectral Method

概要

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This paper presents modification of the Gauss weights accuracy for an optimal control solver using a Jacobipseudospectral method. For the purpose of computing the integral cost term, the accurate Gauss weights at the Jacobi- Gauss-Lobatto points are required. In the case of the specific polynomial approximation, such as the Legendre-Gauss-Lobatto points and the Chebyshev-Gauss-Lobatto points, using their analytic algorithms are sufficient. The method based upon the Vandermonde matrix is suitable for the low-order approximation calculation in the general polynomial case. Due to singularity of the Vandermonde matrix, this method cannot be used in the high-order approximation case. In such case, the modified method which is based upon the High-order Gauss-Lobatto formulae yields high accuracy weights value. Numerical examples demonstrate that this idea yields accurate results.
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