摘要
利用Gr櫣nwald＿Letnicov分数微积分定义计算分数微积分的数值解,计算精度仅为1阶,不能满足快速收敛性要求.给出并证明了分数阶微积分的高阶近似所应满足的条件,并在此基础上推导出分数阶线性定常系统状态空间描述的数值计算公式.本法不但公式简单易编程,而且具有计算精度高、运算速度快等优点.给出一个粘弹性动态系统的仿真实例,验证了其有效性.
The computational precision is only of first order by using Grünwald-Letnicov fractional calculus definition to approximate fractional differentials/integrals,and thus it can not satisfy the high convergence demand.The high order approximate conditions for fractional differentials/integrals are given and verified,and based on that the numerical formula of the state space representation of linear time-invariant fractional order systems is deduced.This algorithm has not only a simple form,which is easy to program,but also the advantage of a high precision and fast computation time.An example of solving numerically the dynamic viscoelasticity system is given to show the effectiveness of the method aforementioned.
出处
《控制理论与应用》
EI
CAS
CSCD
北大核心
2005年第1期101-105,109,共6页
Control Theory & Applications
基金
863基金资助项目(2002AA517020)
上海市科技发展基金资助项目(011607033).
关键词
分数微积分
分数阶系统
分数阶线性多步长方法
状态空间描述
fractional calculus
fractional systems
fractional linear multi-step methods
state-space representation
