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高超声速再入轨迹优化问题是一类复杂的最优控制问题。采用高斯伪谱法(GPM)将再入轨迹优化问题转化为非线性规划问题(NLP),对NLP进行归一化处理后,采用SNOPT软件包求解。根据协态变量映射规则计算出协态变量,得出哈密尔顿函数沿最优控制的变化过程。算例中,GPM耗时约7 s即可生成一条严格满足各种约束的三维最优再入轨迹,耗时远少于相关文献,并且优化精度高,满足一阶最优性必要条件。
Hypersonic reentry trajectory optimization is a complex class of optimal control problems. The recursion trajectory optimization problem was transformed into non-linear programming problem (GPP) by using Gaussian pseudospectral method (GPM). NLP was normalized and solved by SNOPT software package. The covariate variables are calculated according to the covariate mapping rules, and the process of Hamilton function along the optimal control is obtained. In the example, the GPM takes about 7 seconds to generate a three-dimensional optimal reentry trajectory that strictly meets the various constraints, which consumes much less time than the relevant literature and has high optimization accuracy and meets the first-order optimality necessary conditions.