多阶段高斯伪谱法在编队最优控制中的应用

针对编队协同攻击时间最优控制问题，首先通过分析编队协同攻击作战过程，将编队协同攻击任务划分为编队形成、编队保持和协同攻击三个阶段。在简化控制延迟与效率的基础上，建立三阶段通用的空间运动方程。然后结合各阶段的任务特点，综合考虑弹间防碰、期望队形参数、交班误差、导弹自身控制限制，及攻击目标精度等因素，建立各阶段的最优控制模型。基于高斯伪谱法，提出编队形成-保持-攻击一体化的时间最优控制算法。通过大量仿真，在合理选择勒让德-高斯（LG）节点的前提下，利用该方法可快速得到优化的控制指令，弹道及约束性能的仿真结果显示，编队协同攻击全过程可满足任务需求及相应约束限制，校验了算法的可行性。

Application of Multi Phase Gauss Pseudospectral Method in Optimal Control for Formation

In view of the formation coordinated attack time optimal control problem, formation coordinated attack mission is divided into three phases firstly, including formation formed, formation keeping and coordinated attack. Secondly, general motion equations in three phases have been established by simplifying delay and efficiency of control system. Then in combination with the mission characteristics of each phase, an optimal control model is put forward by separately considering anti-collision, expected formation, shift error, control limits, attack accuracy and other factors. To quickly solve the above optimal control problem, based on the Gauss pseudospectral method (GPM), the formation form - keep - attack integrated time optimal control algorithm is presented in this article. Finally, much of simulation work has been done to validate the effectiveness of the method and the simulation results demonstrate that the optimal control instruction can be quickly obtained by using this method under the condition of Legendre-Gauss (LG) nodes be selected reasonably, and the formation coordinated attack process can meet the demand of the task and the corresponding constraints.