低阶实时最优Runge-Kutta算法  

OPTIMAL ALGORITHM OF REAL-TIME RUNGE-KUTTA IN LOW-ORDER

作　　者：黄振全[1] 陈志武[1] 何云[1] 

机构地区：[1]桂林空军学院,广西桂林541003

出　　处：《数值计算与计算机应用》2008年第2期81-88,共8页Journal on Numerical Methods and Computer Applications

摘　　要：在控制系统实时Runge-Kutta算法中,为了满足实时仿真快速性需求,希望尽可能地采用大的计算步长.如果采用大步长,那么数值计算就会引起数值不稳定或者计算误差太大的问题.在现有低阶实时龙格-库塔公式基础上,首先利用RK公式的稳定性方程求解出最大稳定域,然后根据截断误差与相关系数的关系,将其化为一个约束求极小最优问题,并最终推导出实时最优三级二阶RK公式和四级三阶RK公式.仿真结果表明,该算法具有一定的优越性.In real-time Runge-Kutta algorithm for control system, for satisfying the quickness need of real-time simulation, it is expect to choose larger integration step-size. However, the larger step-size would result in the unsteadiness of numerical value and larger error in numeration. So, based on the existing low-order real-time RK formula, using the stability equation of RK formula, the maximum stability region is found. Then, at the basis of the relation of truncation error and related coefficients, a problem of restricted optimization for min is gotten, and the real-time optimum third-grade second-order RK formula and fourth-grade third-order RK formula are deduced finally. The simulation results show that this algorithm is superior in a certain extent.

关 键 词：实时仿真 龙格-库塔算法 最优 稳定域 截断误差 

分 类 号：O232[理学—运筹学与控制论]