基于序列二阶锥优化的多约束最优比例导引研究

鉴于现有制导率难以同时兼顾“最优性”与“满足过程约束”的现状，本课题提出一种新的制导率—“多约束最优比例导引”，该制导率基于导弹与目标之间的相对非线性运动学方程，通过优化传统比例导引中的导引比，不仅使导弹的控制能量最优，还能够满足过程及终端约束条件。为了在线实时计算多约束最优比例导引所对应的非凸最优控制问题，本课题将利用近年来正成为国内外研究热点且具备实时计算能力的“序列二阶锥优化”进行求解，即将原问题转化为迭代求解一系列的二阶锥优化问题（为凸优化问题中的一类特殊问题），该方法涉及如何将原问题转化为二阶锥优化问题、利用最优控制理论分析并保证通过序列二阶锥优化得到的解亦为原问题的解。本项目的研究成果将使导弹能够在线实时计算多约束条件下的最优导引比，提高其对静止或机动目标的打击能力。

Based on the situation that current guidance laws find difficulty in satisfying path constraints and owning optimality simultaneously, this project proposes a new guidance law named “optimal proportional navigation with multiple constraints”. This guidance law, based on the relative nonlinear kinematics between missile and target, chooses to optimize the navigation gain of the traditional proportional navigation. It not only can optimize the control energy, but also can observe path constraints and terminal constraints. To compute the nonconvex optimal control problem related to the guidance law in real-time, we will use the successive second-order cone programming method, which has gained much attention worldwide in recent years and has the capacity for real-time implementation. This approach focuses on how to transform the original problem into a second-order cone program (a special subclass of convex programs), and analyze and guarantee that the solution obtained by successive second-order cone programming is also the solution to the original problem. This project will eventually make a missile have the capacity to compute the optimal navigation gain under multiple constraints, and improve the missile’s performance in attacking both stationary and maneuverable targets.