They have the properties like the quadratic uniform b - spline basis functions . the piecewise polynomial curves generated by the above - mentioned functions possess the same structure and geometry properties as piecewise quadratic uniform b - spline curve 它們具有二次均勻b樣條基函數(shù)的性質(zhì),且用它們生成的分段多項式曲線具有與分段二次均勻b樣條曲線相同的結(jié)構(gòu)和幾何性質(zhì)。
The method employs a recently developed direct optimization technique that uses a piecewise polynomial representation for the state and controls , thus converting the optimal control problem into a nonlinear programming problem . the method is remarkably robust to initial guesses , which is better than traditional method 這種方法利用了近些年來發(fā)展起來的直接優(yōu)化技術(shù),用分段多項式來表示整個軌道的狀態(tài)和控制向量,將最優(yōu)控制問題轉(zhuǎn)化為非線性規(guī)劃問題來研究。
In the computational methods of tpbvp , in order to reduce some difficulties involved in solving a tpbvp via adjoint variables , we discuss a direct method in which state and control variables are indirectly parameterized , the method employs a recently developed direct optimization technique that uses a piecewise polynomial representation for the state and control variables , thus converting the optimal control problem into a nonlinear programming problem , which can be solved numerically . it makes the initial iterative variable more easy to be determined 在數(shù)值解法中,為了減少解決兩點邊值問題共軛變量帶來的困難,主要討論了將狀態(tài)變量和控制變量進(jìn)行參數(shù)化的一種直接方法,這種方法采用了近段發(fā)展起來的使用分段的多項式來代替狀態(tài)和控制變量的直接優(yōu)化方法,然后最優(yōu)控制問題就轉(zhuǎn)化成可以用數(shù)值方法解決的非線性規(guī)劃問題,使得迭代初值更加容易選取。