Optimization of projectile state and trajectory of reentry body considering attainment of carrying aircraft

As an improvement of traditional maximum range trajectory optimization, both the projectile state and control sequence of reentry body are optimized to achieve the maximum range. To ensure the optimal projectile state is in the reachable domain of the carrying aircraft, the climb of the carrying aircraft and the flight of reentry body are optimized as a whole based on the hp-adaptive pseudospectral method. Meanwhile, the path constraints, control constraints and initial/terminal states constraints are considered in the optimization as well. In face of the fact that the range of the optimal control solution resulted from the pseudospectral method may be unsmooth, virtual control variables (second derivatives of the angle of attack and bank angle) are proposed in the optimization, while the angle of attack and bank angle are treated as the virtual state variables to guarantee the smoothness of the optimal control solution. The validity of the virtual control variables in smoothing the optimal control solution is verified by simulation, and the optimality of the resulting projectile state and control sequence for reaching the maximum range is confirmed using the indirect approach.