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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.
Aiming at the pursuit and pursuit of missiles with strong maneuverable warhead during the attack-defense confrontation of missiles, a differential game model of pursuit and evasion of both sides is established and the solution method is given. The first is to give the kinetic model of missile pursuit and escapement; the other is based on differential In this model, the thrust angle is taken as the control variable, the height, the velocity and the longitude angle are regarded as the state variables, and the influence of gravity and rotation of the earth is considered. Thirdly, according to the difficulty of the analytic solution of the model, The high-order fourth-order Gauss-Lobatto polynomial collocation method is given to approximate the nonlinear equations, and the differential equations are transformed into algebraic constraints by discretizing the state variables and control variables at nodes and collocations. Fourth, The concrete method of translating the bilateral optimal strategy into the unilateral optimal strategy is given.Finally the case analysis is carried out to verify the research in this paper.