Midcourse trajectory optimization design for a surface-to-air missile based on Legendre pseudospectral method

To intercept coming targets and to achieve the maximum kill probability, it is necessary to ensure the surface-to-air missile optimal performance at the handover point between the midcourse trajectory and the terminal phase. Several optimal control models were established for the different performance index. The Legendre pseudospectral method was developed to convert the systems containing gap points to nonlinear program (NLP) problems effectively, and the optimal results were obtained by SQP method. Then the objective function of maximum velocity was selected based on the response comparison between the optimal trajectories, and the velocity performance law at the handover point was calculated. The simulation results indicate that the model which is transformed into the NLP problems takes a high optimization precision and fast convergence speed, and the missile velocity at the handover point reaches the maximum value when the pitch and yaw angle are about zero.