Online Optimal Trajectory Generation Algorithm Design based on Backward Recursion

In allusion to the continually changing of predicted handover conditions in midcourse guidance of interception against hypersonic targets, an online trajectory generation algorithm based on neighboring optimal control theory and backward recursion was designed. The nominal trajectory satisfying terminal and path constraints was generated offline by Gauss pseudospectral method (GPM); The first order necessary conditions and transversality conditions of optimal trajectory were further differentiated to obtain perturbation equations. And then the state and co-state modifications and feedback control variables were solved by backward recursion of perturbation equations. The integration step was changed with respect to the variation of flight time. Simulation results show that the modified trajectory by this method is similar to the reoptimized trajectory by GPM in accuracy, but its efficiency is much higher than GPM, which satisfies the online implementation.