高超声速飞行器上升段最优制导间接法研究

Indirect Method of Optimal Ascent Guidance for Hypersonic Vehicle

高超声速飞行器的机身-推进一体化设计使得气动和推进之间存在强非线性耦合,本文针对高超声速飞行器的特点,提出了求解最优上升轨迹的一种可行方案。在零侧滑角和力矩瞬间平衡假设下对上升段飞行问题进行最优建模,将质量引入为状态量,以最省燃料为指标,以推力方向为最优控制量,根据极大值原理推导一阶最优条件。为数值求解两点边值问题,以解析解作为初始猜想,应用经典的有限差分方法和改进的牛顿法,在满足攻角过程约束下,通过同伦算法迭代求解最优轨迹。仿真在给定的初始约束和终端约束下进行,结果表明该制导算法能够实现对高超声速飞行器上升轨迹的优化,以参考面积为同伦参数的迭代方法,能够保证算法的收敛性和快速性。

Hypersonic vehicle has an integrated frame-propulsion configuration.With strong nonlinear coupling between aerodynamic force and thrust,a feasible approach is proposed to obtain the optimal ascent trajectory.Based on zero sideslip assumption the ascent flight problem is modeled by means of optimal control theory.The mass is taken as state variable and the performance index is to minimize fuel consumption.The direction of body longitudinal axis is chosen as control input.The maximum principle is used for optimization.To solve the two point boundary value problem,the analytical mass point solution is taken as initial guess obtained by zero reference area assumption.Both finite difference method and modified Newton method are used to get the numerical solution.With the path constraint of attack of angle,the optimal trajectory is gotten through homotopy algorithm iteration finally.The simulation is conducted under the condition of the given initial and final constraints.The result shows that this method can minimize the fuel consumption for the ascent flight.And the iteration method taking reference area as the homotopy parameter can guarantee convergence of the algorithm.