三维高超声速飞行器再入轨迹快速优化

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。

Rapid approach for three-dimensional trajectory optimization of hypersonic reentry vehicles

Gauss pseudospectral method is used to convert a hypersonic reentry trajectory optimization problem to nonlinear programming(NLP);the NLP is scaled with the method proposed by Betts and then solved by the SNOPT package.The costate variables are obtained through the costate mapping theorem,and the variation of Hamiltonian function along the trajectory is obtained.In the numerical simulation,the Gauss pseudospectral method obtains a constraint three-dimensional optimized reentry trajectory with a time consumption of about 7 seconds,which is far less than that in some published literature.The optimized trajectory is checked of high accuracy,which satisfied the necessary optimal conditions.