Indirect method for trajectory optimization of hypersonic vehicle with static parameters

An indirect method for optimal control problems with static parameters was developed. Trajectory optimization with static parameters for hypersonic vehicle was solved using this method. Static parameters were divided into three kinds, final time, boundary state variables and design variables. The final time can be transferred to a design variable, and convert the free final time problem to a fixed final time problem. The boundary conditions of costates corresponding to the free boundary states can be derived using the maximum value principle. A design variable can be looked as a state variable whose derivative is zero. And new state dynamics, costate dynamics and boundary conditions can be obtained. After that, the optimal control problem with static parameters was converted to a standard two-point boundary value problem (TPBVP). In the end, the wave-rider was taken for example, its aero shape parameters were looked as static parameters. After the aero shape and trajectory integrated optimization, the optimal aero shape was obtained with the global maximum range.