基于伪谱法的滑翔轨迹多级迭代优化策略

Multistage Iterative Optimization Strategy for Gliding Trajectory Based on Pseudo-spectral Method

伪谱法可实时求解具有高度非线性动态特性的飞行器最优轨迹;以X-51A相似飞行器模型为研究对象,采用增量法与查表插值建立纵向气动力模型,伪谱法与序列二次规划算法求解滑翔轨迹最优控制问题;提出使用多级迭代优化策略,为序列二次规划算法求解伪谱法参数化得到的大规模非线性规划问题提供初值,弥补非线性规划问题求解过程中,出现的初值敏感、收敛速度减慢等问题;仿真验证飞行高度、速度、航迹角等状态量基本接近终端设置条件,对比传统方法求解出的飞行状态,偏差明显减少,更加接近最优轨迹;优化目标滑翔距离在相同配点数下,更加接近最优值,配点数越多优化效果越明显,且计算时间大量减少,证明了多级迭代优化策略的有效性和高效性。

The pseudo-spectral method can solve the optimal trajectory of the aircraft with high nonlinear dynamic characteristics in real time.Taking the X-51A similar aircraft model as the research object,the longitudinal aerodynamic model is established by the incremental method and table look-up interpolation.The pseudo-spectral method and the sequential quadratic programming algorithm are used to solve the optimal control problem of gliding trajectory.A multistage iterative optimization strategy is proposed to provide initial values for solving large-scale non-linear programming problems parameterize by pseudo-spectral method,and to compensate for the sensitive initial values and slow convergence of the sequential quadratic programming algorithm in solving large-scale non-linear programming problems.The simulation results show that the state variables such as flight altitude,speed and track angle are basically close to the terminal settings.Compared with the flight states solved by traditional methods,the deviation is obviously reduced and the optimal trajectory is closer.The optimal glide distance of the target is closer to the optimal value under the same collocation points,and the more collocation points,the more obvious the optimization effect,and the calculation time is greatly reduced.The effectiveness and efficiency of the multistage iterative optimization strategy are proved.