A fast matrix generation method for solving entry trajectory optimization problems under the pseudospectral method

A fast matrix generation method based on correlations is proposed for the pseudospectral method (PSM) to solve the entry trajectory optimization problem. First, the optimization problem is analyzed to obtain some assumptions of performance indicators and constraints. Then, the chain rule and correlations among the variables are used to simplify the gradient calculations, resulting in a fast generation method for the gradient vector. Meanwhile, based on the previous assumptions, a fast generation method for the Jacobi matrix is derived semi-analytically using the correlation information among the variables. Finally, the trajectory optimization problem is studied using a typical aircraft. The results are verified via comparisons with the well-known GPOPS II software. Furthermore, the superiority of the proposed method in terms of the computational efficiency is demonstrated by comparing the relevant time indexes. The performance of the proposed method in calculating the Jacobian matrix and gradient matches that of the GPOPS, combined with a relatively short solution time.