奇异摄动法解最优拦截问题

本文应用奇异摄动法探讨水平面内飞机的中远程拦截问题。在介绍航迹优化的一般方法之后,通过采用三重时间尺度分离法建立奇异摄动的数学模型,求出了外层解、边界层解和一致有效的组合解,导出了以推力参数和滚转角为控制变量的最短时间拦截的最优控制律。并以F-4飞机为例,计算了拦截成功的最短时间和最优航迹。其结果可作为空中拦截实时在线优化的参考。

On Solving the Optimal Intercept Problems by the Method of Singular Perturbation

In this paper, a singular perturbation method is applied to solve the intercept problems of aeroplanes in the horizontal plane within intermediate and long ranges. It begins with the introduction of the general methods of flight paths' optimization, then the mathematical model of the singular perturbation is set up by using the separation method of triple time-yardsticks. The outer solution,the boundary solution and the non-condition combinatorial solution are obtained,and the optimal control laws of the interception in the minimum time is reduced with the thrust parameters and the roll angles as their control variables. The paper takes the F-4 aircraft as an example,the minimum time and the optimal flight path for successful intercept are calculated. The result may supply a reference to the.real-time and on-line optimal intercept problems.