最大值原理在制导炸弹滑翔控制中的应用

Application of maximum value principle in gliding control of guided bombs

结合最优控制理论,研究了控制变量和末端状态均有约束的条件下,为了满足某个性能指标最优的要求,制导炸弹的滑翔控制问题。首先,建立了制导炸弹滑翔的最优控制模型。然后,利用最大值原理,引入共轭变量,同时消去控制变量,将最优控制问题转换为微分方程两点边值问题。最后,针对制导炸弹滑翔控制的性能指标以及对末端状态和末端时刻的特殊要求,提出了一种改进的边值打靶法,并通过仿真算例验证了算法的可行性和有效性。

Based on optimal control theory, we studied gliding control of guided bombs for optimizing a certain type of performance index with constraints on control variable and end states. Firstly, the optimal model for guided bomb gliding control is built up. Then, conjugate variables are introduced and control variables are eliminated by using maximum value principle. Therefore, the optimal control is converted into a two-point boundary value issue of differential equations. To meet the performance index requirement to the gliding control, and the special end-state and temporal constraints, the shooting method is modified. An example for guided bomb optimal gliding is given to validate the effectiveness of proposed method.