基于析取关系直接变换的冲突解脱方法
收稿日期: 2013-08-20
修回日期: 2013-12-25
网络出版日期: 2014-01-07
基金资助
国家自然科学基金（61203132）
Direct Disjunction Transcription Based Conflict Resolution Approach
Received date: 2013-08-20
Revised date: 2013-12-25
Online published: 2014-01-07
Supported by
National Natural Science Foundation of China (61203132)
针对自由飞行条件下的飞行冲突解脱问题，提出了一种基于析取关系直接变换的联立求解方法（DDTSA）。首先在不引入额外辅助变量的情况下，将基于析取关系的安全边界条件变换成易于联立求解的约束条件，使问题的变量和方程个数大幅度减少，从而降低问题的求解难度。然后为保证求解的精度和稳定性，采用基于Radau配置点的拉格朗日插值多项式对微分代数方程组进行离散化处理，继而求解离散化得到的非线性规划问题。最后分别对2架、3架以及4架飞机的冲突解脱问题进行仿真，仿真结果表明与相关文献中的方法相比，该方法具有更高的计算效率并且能够得到更优的结果。
陈伟锋 , 邵之江 . 基于析取关系直接变换的冲突解脱方法[J]. 航空学报, 2014 , 35(4) : 1122 -1133 . DOI: 10.7527/S1000-6893.2013.0505
For the conflict resolution under free flight conditions, a direct disjunction transcription based simultaneous approach (DDTSA) is put forward in this paper. First, the disjunction based safety boundary conditions are transformed directly into continuous constraints without introducing any additional auxiliary variables, which can be handled simultaneously with ease. The number of variables and the number of equations can be decreased remarkably and then the solution difficulty is reduced. In order to guarantee the solution precision and the solving stability, Radau collocation points based Lagrangian interpolation polynomial is utilized to discretize the group of differential algebraic equations, and then the generated nonlinear programming program is solved to obtain the optimal control profiles. Finally, two aircrafts, three aircrafts and four aircrafts conflict resolution problems are demonstrated. The simulation results show that the proposed method is able to solve these conflict resolution problems with higher efficiency than the approach presented in the related reference; furthermore, it can also yield a better objective value.
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