Optimal Ascent Guidance for Air-Breathing Launch Vehicle Based on Optimal Trajectory Correction
Optimal Ascent Guidance for Air-Breathing Launch Vehicle Based on Optimal Trajectory Correction
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DOI：
10.1155/2013/313197
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发表时间：
2013-12
影响因子：
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通讯作者：
Xuefang Lu;Yongji Wang;Lei Liu
中科院分区：
文献类型：
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作者：
Xuefang Lu;Yongji Wang;Lei Liu
提出了一种基于最优弹道修正的吸气式运载火箭最优制导算法。最优轨迹修正问题是一个带状态不等式约束的非线性最优反馈控制问题，其结果是一个非线性的、不可微的两点边值问题。车载TPBVP问题的求解比较困难。为了降低在星计算成本，该制导算法在每个制导周期内对参考轨迹进行修正，以满足最优反馈控制问题的最优性条件。通过线性化最优性条件，得到了用于最优弹道修正的线性TPBVP。线性TPBVP的解是通过Simpson法则求解线性方程组得到的。将线性TPBVP的解作为校正值的搜索方向，通过线性搜索产生更新步长。将光滑逼近应用于不可微哈密顿量的不等式约束。给出了算法全局收敛的充分条件。最后，仿真结果表明了该算法的有效性。
An optimal guidance algorithm for air-breathing launch vehicle is proposed based on optimal trajectory correction. The optimal trajectory correction problem is a nonlinear optimal feedback control problem with state inequality constraints which results in a nonlinear and nondifferentiable two-point boundary value problem (TPBVP). It is difficult to solve TPBVP on-board. To reduce the on-board calculation cost, the proposed guidance algorithm corrects the reference trajectory in every guidance cycle to satisfy the optimality condition of the optimal feedback control problem. By linearizing the optimality condition, the linear TPBVP is obtained for the optimal trajectory correction. The solution of the linear TPBVP is obtained by solving linear equations through the Simpson rule. Considering the solution of the linear TPBVP as the searching direction for the correction values, the updating step size is generated by linear search. Smooth approximation is applied to the inequality constraints for the nondifferentiable Hamiltonian. The sufficient condition for the global convergence of the algorithm is given in this paper. Finally, simulation results show the effectiveness of the proposed algorithm.