A Comparison of Accuracy and Computational Efficiency of Three Pseudospectral Methods

A comparison is made between three pseudospectral methods used to numerically solve optimal control problems. In particular, the accuracy of the state, control, and costate obtained using the Legendre, Radau, and Gauss pseudospectral methods is compared. Three examples with different degrees of complexity are used to identify key differences between the three methods. The results of this study indicate that the Radau and Gauss methods are very similar in accuracy, while both significantly outperform the Legendre method with respect to costate accuracy. Furthermore, it is found that the computational efficiency of the three methods is comparable. Based on these results and a detailed analysis of the mathematics of each method, a rationale is created to determine when each method should be implemented to solve optimal control problems.

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