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针对运载器大气层内的最优轨迹快速规划问题,提出一种将求解最优控制问题的间接法与直接法相结合的混合优化方法。首先,基于最优控制问题的一阶必要条件,将运载器大气层内的三维最优上升问题转化为Hamiltonian两点边值问题;然后,采用直接法中能以较少的节点获得较高求解精度的Gauss伪谱法进行求解,提高算法的求解效率;最后,采用真空解析解初值及密度同伦技术,解决初值猜测与算法收敛困难的问题。仿真结果表明,混合优化算法能够准确、快速地对运载器大气层内的最优上升轨迹问题进行求解,并在计算精度与效率上均优于间接法,可应用于运载器的轨迹在线规划与闭环制导。
Aiming at the problem of rapid programming of the optimal trajectory in the atmosphere of the carrier, a hybrid optimization method combining the indirect method and the direct method to solve the optimal control problem is proposed. First, based on the first-order necessary condition of the optimal control problem, the three-dimensional optimal rise problem in the atmosphere of the carrier is transformed into the Hamiltonian two-point boundary value problem. Then, the direct solution method can obtain higher solution accuracy with fewer nodes Gauss pseudospectral method to improve the efficiency of the algorithm. Finally, the initial value and density homotopy technique are used to solve the problem of initial guess and algorithm convergence. The simulation results show that hybrid optimization algorithm can solve the optimal ascending trajectory accurately and quickly in the atmosphere of the carrier, and is superior to the indirect method in the accuracy and efficiency of calculation. It can be applied to the on-line planning and closed-loop Guidance.