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用对角化乘子法(DMM)解决了三维弹道最优化问题,其中使用了Tapia-Han 乘子校正公式,而未沿用 BFGS Hessian 校法正。对角化乘子法是一种非线性规划的单一步骤最小值算法,避免了经典增广拉格朗日法本身一系列的求最小值问题。为不对 DMM 的初始乘子修正过多,提出了一种沿 Han-Tapia 乘子校正方向使 Kuhn-Tucker 向量范数减至最小的新的修正法。PYOPT 软件包由印度空间研究机构(ISRO)研制并进行验证,它是应用对角化乘子法对运载火箭弹道有约束俯仰和偏航控制律进行优化。弹道最优化的系统动态模型为有效地和常规研究创造了条件。用非线性规划的最优性充分条件借助于鞍点最优性理论和增广性理论建立了 PYOPT 的最优解法。软件包的实用性已被证实。目前该软件包已成为印度空间研究机构飞行设计研究的标准工具,它比依据投影梯度法和递归二次规划这类程序的运算速度快得多。
The 3D trajectory optimization problem was solved using the diagonalized multiplier method (DMM), using the Tapia-Han multiplier correction formula instead of using the BFGS Hessian correction. Diagonalization multiplier method is a non-linear programming single-step minimum algorithm, to avoid the classical Augmented Lagrange method itself a series of minimum value problem. In order not to overcorrect the original multiplier of the DMM, a new correction method is proposed to minimize the Kuhn-Tucker vector norm in the Han-Tapia multiplier correction direction. The PYOPT package, developed and validated by the Indian Space Research Agency (ISRO), is a diagonalized multiplier method that optimizes the launch vehicle’s constrained pitch and yaw control laws. The ballistic-optimized system dynamics model creates the conditions for effective and routine research. The optimal solution of PYOPT is established by means of the saddle point optimality theory and augmented theory by using the sufficient condition of the optimality of nonlinear programming. The practicality of the package has been confirmed. At present, the software package has become the standard tool for flight design research conducted by the Indian Institute of Space Studies and is much faster than procedures based on such methods as projection gradient and recursive quadratic programming.