一种基于θ-D次优控制的三维末制导律设计

θ-D Approach-Based Design of 3-Dimensional Terminal Guidance Law

最优制导律在求解Hamilton-Jacobi-Bellman(HJB)方程时十分困难。θ-D方法是一种基于State Dependent Riccati Equation(SDRE)方法的新型次优控制方法,能够获得HJB偏微分方程的近似闭环解。针对最优制导律在求解HJB方程时十分困难的问题,文章在考虑导弹自动驾驶仪动态特性和末制导的三维真实拦截情况下,建立导弹和目标的三维相对运动方程,基于θ-D次优控制方法,经状态重定义后对模型方程的伪线性化处理,得到闭环形式的θ-D三维末制导律。为验证所提出制导律的制导性能,分别针对目标不机动和机动的拦截情况进行了数值仿真。仿真结果表明,相比自适应变结构制导律,文中设计的θ-D三维闭环末制导律能克服自动驾驶仪动态延迟对制导性能的影响;对于目标作大机动逃逸的情况,其制导性能更优。

One of the terminal guidance problems based on optimal control is solving Hamilton-Jacobi-Bellman（HJB） partial differential equations.The θ-D method is a new suboptimal control method based on the State Dependent Riccati Equation（SDRE） method,and has proven to be effective in solving the HJB equations approximately.A suboptimal terminal guidance law is thus proposed for missiles intercepting maneuvering targets based on the θ-D method.Sections 1,2 and 3 of the full paper explain our proposed method,whose core consists of： ＂ The kinematical equations of the guidance problem is first formulated in the 3-dimentional space considering the autopilot lag;then,by redefining the state variables and transforming the nonlinear kinematics equations into a linear-like structure,a closed form guidance law is then derived based on the θ-D method.＂ Finally,to verify the proposed guidance law,numerical simulations in section 4 respectively for intercepting the non-maneuvering and maneuvering targets are made;the simulation results,presented in Figs.2 through 4 and Table 1,and their analysis demonstrate preliminarily that,compared with the adaptive sliding mode guidance（ASMG） law,the proposed guidance law is more effective in compensating for the bad influence of the autopilot lag on guidance accuracy.