Improved parameterization method and its application on solving optimal control problem

The mathematics fundamentals of solving optimal control(OC) problem by parameterization method is easy to be understood, but a nonlinear programming(NLP) problem is usually hard to be solved because the dimension derived from parameterization method are too high. The characteristics of improved method is that only parameterizes the control variables. The dimensions of a NLP problem will be reduced greatly if the improved parameterization method is employed, then the problem will become easy to solve. The improved method has been successfully applied to solve a problem of an aircraft optimal landing trajectory in penetrating wind shear.