带静态参数的高超声速飞行器轨迹优化算法

提出了一种求解带静态参数最优控制问题的间接算法，解决了带静态参数的高超声速飞行器轨迹优化问题.将最优控制中的静态参数分为3类：终端时间、边界点状态变量和设计变量.通过转换公式，可以将终端时间变为优化过程中的一个设计变量，终端时间可变问题转换为终端时间固定问题.边界点状态变量自由，可以根据极大值原理推导获得相应的协态边界条件.设计变量可以看作是导数为零的状态变量，从而获得新的状态方程和协态方程，以及初始和终端对应设计变量的协态值.经过变化，带静态参数的最优控制问题构成一个标准两点边值问题.最后以乘波体为研究对象，将气动外形参数作为优化静态参数，完成了外形/轨迹一体化优化设计，获得了满足全局最大航程要求的最优气动外形.

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.