Direct trajectory optimization based on a mapped Chebyshev pseudospectral method

doi:10.1016/j.cja.2013.02.018

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Direct trajectory optimization based on a mapped Chebyshev pseudospectral method

2013-04-01

Xiao Guo

Ming Zhu *

DOI：10.1016/j.cja.2013.02.018

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Abstract

En 中文

In view of generating optimal trajectories of Bolza problems, standard Chebyshev pseudospectral (PS) method makes the points' accumulation near the extremities and rarefaction of nodes close to the center of interval, which causes an ill-condition of differentiation matrix and an oscillation of the optimal solution. For improvement upon the difficulties, a mapped Chebyshev pseudospectral method is proposed. A conformal map is applied to Chebyshev points to move the points closer to equidistant nodes. Condition number and spectral radius of differentiation matrices from both methods are presented to show the improvement. Furthermore, the modification keeps the Chebyshev pseudospectral methods advantage, the spectral convergence rate. Based on three numerical examples, a comparison of the execution time, convergence and accuracy is presented among the standard Chebyshev pseudospectral method, other collocation methods and the proposed one. In one example, the error of results from mapped Chebyshev pseudospectral method is reduced to 5% of that from standard Chebyshev pseudospectral method. (c) 2013 Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA.

Keywords:

Chebyshev approximation

Conformal shift

Interpolation

Optimization

Pseudospectral method

Trajectory

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