防空导弹最优弹道的协态估计优化算法

Co-state estimation algorithm of the surface-to-air missile optimal trajectory

为了快速精确地得到防空导弹中段最优弹道,在拟勒让德谱变换法的基础上提出了协态估计优化算法.该算法克服了采用拟勒让德谱变换法所得非线性规划NLP(Non-Linear Programm ing)问题优化变量过多、收敛速度慢的缺点,并能在避免求解两点边值问题TPBVP(Two Point Boundary Value Problem)的前提下,快速解得近似满足最优解必要条件的解.针对防空导弹中段弹道优化问题的特点,应用提出的协态估计优化算法进行优化得到结果,与拟勒让德谱变换法所得结果相比,表明该算法具有收敛速度快,优化精度高的优点.

As to obtain the precise optimal trajectory of the surface-to-air missile rapidly, a co-states estimation optimization algorithm was developed based on the Legendre pseudospectral method. The algorithm overcomes the shortcoming of the Legendre pseudospectral method such as there are too many optimization variables in the nonlinear programming （NLP） problem and the slow convergence rate. Additionally, on the premise of avoiding solving the two point boundary value problem （TPBVP）, the optimal results satisfying the es- sential conditions could be computed rapidly. According to the characteristics of the midcourse trajectory optimization problem for a surface-to-air missile, the co-state estimation algorithm and the Legendre pseudospectral method were applied, and the results show that the algorithm takes on fast convergence rate and high optimization precision.