带有双曲正切加权函数的落角约束最优制导律

Impact angle constrained optimal guidance law based on hyperbolic tangent weighting functions

摘要:

为降低末制导律对初始状态误差的敏感度、提高导弹的末端抗干扰能力,针对带有落角约束的末制导问题,考虑基于双曲正切函数的一类加权函数,提出了一种基于间接Gauss伪谱法的最优末制导律. 首先,基于目标位置和期望落角建立了落角坐标系,并在该坐标系中建立了导引运动关系方程,得到了带有落角约束的末制导模型；然后,根据极小值原理推导出了用于求解最优制导律的两点边值问题,运用Gauss伪谱法进行离散,把两点边值微分方程转换为一系列代数方程；最后,通过显式求解代数方程快速得到了最优控制律,该方法避免了求解黎卡提微分方程,不需要进行繁琐的积分运算,计算量小. 所提制导律在推导过程中不依赖于加权函数的具体形式,可非常方便地处理复杂加权函数. 仿真结果表明:通过设计不同形式的加权函数,可灵活改变导弹运动轨迹及制导指令的分布,以实现不同的制导目标；所提方法能有效降低制导律对初始状态误差的敏感度,而且还可以提高导弹的末端抗干扰能力,在很大程度上提高了制导律的设计灵活性.

Abstract:

To alleviate the sensitivity of homing guidance with respect to initial state errors and enhance the anti-disturbance capability of missile at the final time, this paper presents an optimal guidance law with impact angle constraint based on a class of hyperbolic tangent weighting function using the indirect Gauss pseudospectral method. First, an impact angle coordinate system was established based on the desired impact angle and the position of the target, in which the motion kinetics for the engagement was constructed and the homing guidance model with impact angle constraint was obtained. Second, the two-point boundary problem was derived by utilizing the minimum principle, which was then discretized into a set of algebraic equations by employing the Gauss pseudospectral method. Finally, the optimal guidance law was easily obtained via explicitly solving the algebraic equations. This approach does not need to solve the Riccati differential equations and avoids cumbersome integral operations, which leads to a low computational load. The derivation of the proposed guidance law does not rely on the concrete form of weighting functions, and it can handle complex weighting functions. Simulation results demonstrate the performance of the proposed guidance law and show that the trajectory and acceleration command of missile could be shaped as desired by employing different types of weighting functions. The proposed algorithm could effectively reduce the sensitivity of homing guidance with respect to initial state errors and ensure the operational margin to cope with external disturbances at the end of the homing phase, provides more degrees of freedom in the guidance law design to accomplish specified guidance objectives.