2011 Volume 77 Issue 784 Pages 4458-4467
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.
Transactions of the Society of Mechanical Engineers
Transactions of the Japan Society of Mechanical Engineers
Transactions of the Japan Society of Mechanical Engineers Series A
Transactions of the Japan Society of Mechanical Engineers Series B
Transactions of the Japan Society of Mechanical Engineers Series C
TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A
TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B
