飞行器上升段轨迹的优化设计

The Optimization of the Design of Ascent Trajectory of a Vehicle

针对飞行器上升段轨迹优化求解困难的问题,提出一种基于正交配点的优化求解方法。该方法以第二类切比雪夫正交多项式的零点作为系统控制变量和状态变量的离散点,利用拉格朗日插值多项式对状态和控制变量进行拟合。通过对多项式的求导将动力学微分方程约束转化为代数约束,从而把无限维的最优控制问题转化为一个有限维的非线性规划(Nonlinear Programming,NLP)问题。随后,利用序列二次规划(Sequential Quadratic Program-ming,SQP)方法求解转化后的NLP问题,获得最优的飞行轨迹。最后,飞行器上的仿真结果验证了所提方法的有效性。研究成果可为飞行器的制导控制提供可行的飞行轨迹,有一定的工程应用价值。

A new method based on orthogonal collocation is proposed to deal with the difficulty of solving the ascent trajectory optimiza- tion problem. Lagrange polynomial is employed to approximate the state and control variables which are discrete values from the zeros of the second Chebyshev polynomial. The constraints of the dynamic differential equations can be transformed into algebraic equation con- straints by deriving the polynomial. As a result, the infinite dimensional optimal control problem is converted to a finite dimensional nonlinear programming （NLP） problem. Following that, the transformed problem can be solved by the sequential quadratic program- ming （SQP） method to obtain the optimal trajectory of a vehicle. Finally, simulation results verify the effectiveness of the proposed method. The results of this study can provide feasible flight trajectory for the guidance and control of a vehicle. Besides that, the appli- cation of this method to engineering is also valuable.