针对拦截弹道设计时多阶段、飞行时间可变且要满足复杂约束的最优控制问题,采用高斯伪谱法进行求解。与其它数值方法相比,高斯伪谱法把最优控制问题分解成不同的阶段,利用多项式拟合避免积分过程,提高了优化效率。进而把拦截时间转化为优化变量,解决了拦截时间可变问题,详细描述了拦截弹道设计问题,最后给出了仿真算例和结果分析。 Aiming at the problem of multi-stage interception trajectory design, variable flight time and the optimal control problem to meet the complex constraints, the Gaussian pseudospectral method is used to solve the problem. Compared with other numerical methods, the Gaussian pseudospectral method decomposes the optimal control problem into different stages and uses polynomial fitting to avoid the integral process, thus improving the optimization efficiency. Then the interception time is transformed into optimization variables to solve the problem of variable interception time. The problem of interceptor trajectory design is described in detail. At last, simulation examples and results analysis are given.