导弹追逃博弈微分对策建模与求解

针对导弹攻防对抗过程中拦截器追击具备较强机动能力弹头的追逃问题,建立了双方追逃微分对策模型并给出求解方法.一是给出导弹追逃质点动力学模型;二是基于微分对策理论,建立了导弹攻防对抗微分对策模型,模型以推力角为控制变量,高度,速度和经度角为状态变量,并考虑了地球重力和自转的影响;三是针对模型获得解析解的困难,给出高精度四阶Gauss-Lobatto多项式配点法来逼近非线性方程,通过离散化节点和配点上的状态量和控制量将微分方程组转换为代数约束;四是为采用配点法求解模型,给出了将双边最优对策问题转化为单边最优对策问题的具体方法.最后实例分析对本文研究进行了仿真验证.

Differential game model and solving method for missile pursuit-evasion

For the pursuit-evasion game of an interception missile (interceptor) pursuit an incoming ballistic missile (warhead), each missile was given a modest post launch capability to maneuver, differential model and solving method of the game was proposed. Firstly, we gave a mass-point dynamics model of the missile pursuit-evasion system. Secondly, based on differential game theory, we established the detailed differential game model of missile pursuit-evasion problem. The model took thrust angle as control variable and flight height, velocity, longitude as state variables, it also considered earth gravity and rotation effects. Thirdly, as differential game can hardly solved analytically, we gave numerical solving method that employed fourth degree Gauss-Lobatto quadrature rule to improve accuracy when compared with lower degree rules such as Simpson's rule, at the nodes and collocation points the values of the state and control were discrete to transform differential equations to algebraic equations. Fourthly, we gave the method able to transform a two-side differential game into a single objective problem. Experimental study verified the model and solving method proposed.