Optimization of Projectile State and Trajectory of Reentry Body Based on Hp-adaptive Pseudospectral Method

Considering the path constraints, control constraints and initial/terminal states constraints, optimal projectile state and trajectory of reentry body are designed based on hp-adaptive pseudospectral method to achieve maximum range. Path constraints include normal overload constraint, dynamic pressure constraint and heating rate constraint; control constraints include angle of attack constraint and bank angle constraint; initial/terminal states constraints include altitude constraint, velocity constraint and flight path angle constraint. In face of the fact that the range of optimal control solution resulted from 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 hp-adaptive pseudospectral method in dealing with nonlinear, multi-constrained, multi-variable optimization problems is verified by simulation, and the consistency between the solution obtained and the first-order necessary conditions for optimality of indirect method is confirmed using the costate and Hamiltonian.