无惩罚SQP方法在动力下降制导问题中的应用

Application of Penalty-Free SQP Method in Powered Descent Guidance Problem

摘要: 序列二次规划(SQP)方法是一个较为实用的求解非线性约束优化问题的方法。本文提出了一种基于无惩罚框架的改进的SQP算法。该算法不涉及罚函数，不需要考虑罚因子的选取，也不需要滤子和可行性恢复阶段。提出的算法能够克服二次规划子问题的不相容性，并且迭代点列关于目标函数和约束函数是非单调的。在有界性假设条件下，算法具有全局收敛性。当原问题无解时，算法可以收敛到原问题的不可行稳定点。此外，本文建立了动力下降制导问题的数学模型，以燃油消耗质量最低为目标，给出了算法的仿真结果和分析。

Abstract: The Sequential Quadratic Programming (SQP) method is a practical approach for solving nonlinear constrained optimization problems. This paper proposes an improved SQP algorithm based on a penalty-free framework. The algorithm eliminates the need for penalty functions, avoids considerations of penalty factors, and dispenses with filters and feasibility restoration phases. The proposed algorithm addresses the compatibility of quadratic programming subproblems and ensures that the iterates are non-monotonic with respect to both the objective function and constraint functions. Under boundedness assumptions, the algorithm exhibits global convergence. In cases where the original problem is infeasible, the algorithm can converge to infeasible stationary points of the original problem. Additionally, this paper establishes a mathematical model for the descent guidance problem, aiming to minimize fuel consumption, and provides simulation results and analysis of the algorithm.