脱靶量及其变化率双重加权的微分对策制导律

Dual-weighted differential game guidance law for miss distance and its rate of change

摘要:

为进一步增强导弹飞行弹道的收敛速度,定义末端的脱靶量和脱靶量变化率作为性能优化指标,并基于线性二次型微分对策理论进行了制导律的推导,推导结果实现了减少脱靶量的同时向着最大化脱靶量收敛速度的方向上进行控制的目的。本研究从一般意义上进行导弹和目标控制系统动态特性的建模,适用于二者具有高阶控制系统动态特性的形式,推导结果具有一般性。针对导弹和目标具有一阶控制系统动态特性的情况,进行了制导律的扩展,并相应完成了对策空间的分析和典型制导参数的取值分析。非线性系统仿真针对比例导引、典型微分对策制导律和本研究所提出的脱靶量及其变化率双重加权的微分对策制导律进行了对比分析,仿真情形包括目标常值机动、S型机动和随机机动3种情形,并采用单发命中概率作为制导性能衡量指标。结果表明,所提出制导律的弹道快速收敛性能和低过载需求,在最小化脱靶量的同时最大化脱靶量的收敛速度,实现了在拦截导弹飞行弹道快速收敛的方向上进行控制的目的。

Abstract:

To further improve the rate of trajectory convergence, terminal miss distance and miss distance rate are defined as performance index for guidance law derivation based on linear quadratic differential game theory. The derivation results realize the control purpose of minimizing miss distance while maximizing miss distance convergence rate. The control systems of intercept missile and its target are modeled in a general sense, applicable to forms where both exhibit higher-order dynamic characteristics. The derivated guidance law has a wide general adaptability. The proposed guidance law is extended to the typical situation of missile and its target with one-order control system dynamics. A comparative analysis of nonlinear system simulations has been performed for proportional navigation, conventional differential game guidance law, and the dual-weighted differential game guidance law proposed in this study. The simulation scenarios include three types of maneuvers: constant-maneuvering, S-type maneuvering and random starting maneuvering of target. The single shot kill probability is used for guidance performance evaluation. The simulation results show the advantages of fast trajectory convergence rate and low acceleration requirements of the proposed guidance law. The proposed guidance law minimizes the miss distance while maximizing the trajectory convergence rate of the miss distance, achieveing the control purpose of fast trajectory convergence of interception missile.