基于零和微分对策的非仿射导弹拦截系统制导律设计

Design of Guidance Law for Non-affine Missile Interception System Based on Zero-sum Differential Game

文中基于零和微分对策理论研究了非仿射导弹拦截系统制导律设计问题。首先构建辅助系统,将系统转化为仿射非线性增广形式;其次将导弹与目标视为对抗双方,根据极大极小值原理,设计最优微分对策制导策略,使得拦截系统能够满足预设的性能指标;接着为了获得HJI(Hamilton-Jacobi-Isaacs)方程解析解,利用积分自适应动态规划技术构建神经网络;然后设计积分型自适应权值更新律,在线学习最优微分对策制导律,通过Lyapunov方法证明了闭环系统的有界性;最后将所提算法应用于非仿射导弹拦截系统。仿真结果表明,导弹视线角速率和相对速率满足目标成功捕获必要条件且脱靶量为1 m左右,导弹能够成功拦截目标。

In this paper,the problem of guidance law of non-affine missile interception system is studied based on zero-sum differential game theory.Firstly,an auxiliary system is constructed and the system is converted into affine nonlinear augmented form.Secondly,the missile and target are regarded as competitors and the optimal differential game guidance strategy is designed based on the maximin principle to make the system meet the predefined performance index function.Subsequently,to obtain the analytical solution of the HJI(Hamilton-Jacobi-Isaacs)equation,the integral adaptive dynamic programming technique is used to develop the neural network.Then,the integral adaptive weight updating law is designed to learn the optimal differential game guidance law online and the closed-loop system is proved to be bounded by Lyapunov theory.Finally,the proposed method is applied to the non-affine missile interception system.The simulation results indicate that the line of sight angle rate and range rate satisfy the necessary condition for successful target capture.In addition,the minimum terminal zero effort miss distance is about 1 m.These demonstrate that the target can be intercepted successfully and the proposed method is effective,the missile can successfully intercept the maneuvering target and the proposed algorithm is shown its effectiveness.