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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.
An indirect algorithm to solve the optimal control problem with static parameters is proposed to solve the hypersonic vehicle trajectory optimization problem with static parameters.The static parameters in the optimal control are divided into three categories: terminal time, state variables of boundary point and Design variables, the terminal time can be transformed into a design variable in the optimization process, the terminal time variable problem can be converted into a terminal time fixed problem by the conversion formula.The boundary point state variables are free and can be derived according to the principle of maximum value State boundary conditions. Design variables can be seen as state variables with zero derivatives to obtain new state equations and co-equation equations, as well as coherency values for the initial and terminal design variables. After the change, the optimal control with static parameters The problem constitutes a standard two-point boundary value problem.Finally, taking the wave body as the research object, taking the aerodynamic shape parameters as the optimization static parameters, the shape / trajectory integration optimization design is completed and the optimal aerodynamic shape satisfying the global maximum range requirement is obtained .