针对新型战术弹道导弹(TBM)和智能巡航导弹等具有高机动性的拦截目标,应用控制受限的非线性对策模型,提出非线性微分对策制导律,并分析了零脱靶量拦截所容许的初始航向误差。目标和拦截弹间的相对运动是非线性的,采用传统线性化模型建立的拦截制导律会因为线性化而带来误差。提出的制导律是在保持拦截弹和目标的非线性运动学关系的基础上,把拦截弹航向误差作为性能指标,基于反馈线性化的思想,应用最优控制理论建立的。应用该制导律研究了在迎击拦截、追击拦截和阻击拦截3种拦截方式下实现零脱靶量拦截的容许初始航向误差,分析结果表明减小相对运动速度、提高拦截弹的机动加速度可以增加容许的初始航向误差。同时,当拦截弹具有速度优势时,目标的初始前置角接近90°或采用追击拦截可以允许较大的初始航向误差。
This paper develops a guidance law for the interceptors against highly maneuverable targets, such as tactical ballistic missiles (TBM) and cruise missiles with intelligent control systems, by using a nonlinear differential game formulation with bounded controls. It also analyzes the admissible initial flight-path errors of perfect intercept. Since the kinematics of the relative motion between the target and the interceptor is actually nonlinear, guidance laws traditionally based on linearization cause errors in the interception. In this paper, the guidance law is proposed by using nonlinear kinematics, taking the flight-path error of the intercept missile as the performance function and utilizing the feedback linearization and optimal control theory. The admissible initial flight-path errors of perfect intercept are studied in three intercept cases: head-on intercept, tail-chase intercept, and head-pursuit intercept. The results show that a smaller closing velocity and a greater maneuver acceleration of the intercept missile lead to a bigger admissible initial flight-path error. If the intercept missile possesses the advantage of velocity, a bigger admissible initial flight-path error can also be tolerated when the lead-angle of the target approximates 90°, or when the tail-chase mode of intercept is adopted.
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