A Study on the Numerical Method for Simultaneous Optimization of Spaceplane Design and its Flight Trajectory.

The numerical method to solve simultaneous design and control optimization problems is considered. Firstly, the simultaneous optimization problem dealt with in this paper is defined, and this problem is transformed into a new formulated nonlinear programming problem. Considering that the nonlinear programming problem is solved by using a sequential quadratic programming method, the diagonal form of the Hessian matrix for the Lagrange function is introduced in a new formulation named Block Diagonal Hessian (BDH) method. Secondly, the BDH method is applied to the simultaneous spaceplane design and trajectory optimization problem, where the best size and its optimal trajectory are estimated to realize it. Through the several calculations, it is confirmed that the proposed BDH method is effective for simultaneous design and control optimization problems.