Notice of Retraction: Gliding trajectory optimization based on hp-adaptive pseudospectral method

Trajectory design plays an important role in the overall design optimization of an aero-craft. As a classic method to solve trajectory optimization design problem, the indirect method is complex and very sensitive to the initial guesses of castrates. As opposed to indirect method, the direct method is convenient and can obtain the optimal solution with higher probability. Therefore, in the present paper, the recently developed direct method, hp-adaptive pseudospectral approach, is applied to a gliding trajectory optimization problem to generate an optimal gliding trajectory yielding maximum range. However, it has been frequently noticed that the direct method may end up with suboptimal or even poor solution since it is only an approximation of the original optimal control problem, which cannot be adopted in engineering and needs to be verified beforehand. To address this issue, the indirect method is employed to verify the optimality of the solution from the hp-adaptive pseudospectral method. Simulation results show that the verified optimal solution meets the dynamic constraints well and evidently improves the range compared to the original trajectory.