改进参数化方法及在低空风切变中的应用

Improved parameterization methods and its application in wind shear in low altitude

研究对参数化方法进行必要的改进,从而使该方法更好地用于求解最优控制问题。改进的基本思路是设法降低利用该方法转换而得的非线性规划子问题的维数。通常在利用参数化方法求解最优控制问题时,由于对控制变量和状态变量同时参数化,从而导致所转化而得的非线性规划子问题维数高,求解难。通过分析认为,只需对控制变量参数化,而对状态变量在时间节点处的值,则可通过对最优控制问题的微分约束进行分段积分求得,从而降低了转换而得的非线性规划子问题的维数,有利于该算法进一步推广应用。利用改进算法求解了飞机在低空风切变中的最优着陆轨迹问题,求解结果表明,改进算法可以顺利求解一类最优控制问题。

study how to improve parameterization method in this paper so that it is easier to be applied in solving optimal control problem.The way to improve the algorithm is that manage to decrease the dimensions of the sub-problem of non-linear programming（NLP）derived from the parameterization method.When the optimal control problem is solved with parameterization method,the control and state variables are usually parameterized together.And this will lead to a high dimension sub-problem of NLP,so it is not easy to be solved.After study the mathematics fundamentals of parameterization method deeply,a new method of improving parameterization algorithm is put forward,i.e.it is enough to parameterize control variables of a optimal control problem,and the values of state variables at time knots can be obtained through integrating the differential constraints of each section of the problem.The improved method decreases the dimensions of the sub-problem of NLP,so it is easy to be solved and it is helpful to make parameterization method apply in solving some optimal control problem widely.The improved method is applied in solving optimal landing trajectory problem of an aircraft in wind shear,and the results show that some optimal control problem can be solved smoothly with the new method.