导弹攻防对抗中追逃对策模型与配点求解法

摘要

Future incoming missiles may have a large maneuvering potential and can perform random ma-neuvers,rendering their trajectory unpredictable.For the pursuit-evasion game of an interceptor tries to inter-cept ballistic missile warhead,the pursuit-evasion game based differential game (DG)theory is modeled and the collocation solving method is given.The differential equations model takes the thrust angle as control variable and flight height,velocity,longitude as state variables,it also considers earth gravity and rotation effects.We transform the two-side DG problem into a single objective problem,and then give the collocation solving meth-od.The method employs the fifth degree Gauss-Lobatto quadrature rule with improved accuracy to approximate describe the time derivative of state,after that we transform differential equations to algebraic equations.Ex-perimental study verifies the model and the proposed method.%未来的来袭导弹可能具备较强的机动性，其弹道不可预测，针对拦截弹追击此类目标的追逃问题，基于微分对策（differential game，DG）理论建立追逃博弈模型并给出求解方法。模型在分析两者相对运动的基础上，考虑地球重力和自转的影响，以推力角为控制变量，离地高度、速度和经度角为状态变量，建立微分方程组。然后将追逃 DG 模型转化为单边最优对策问题；并给出改进的高精度五阶 Gauss-Lobatto 多项式配点法来近似状态变量对时间的导数，将微分方程组转换为代数约束，降低非线性规划问题复杂程度。最后给出了本文研究的仿真实例。