一类分数阶控制系统的数值解法

Nynerucal Methods for a Fractional-order Control System

着重考虑4项的分数阶动力控制系统的微分方程.证明了其解的存在性与惟一性,并用Mittag Leffle函数将解表示出来,但其解析解是很难数值地求出的.利用Caputo,Riemann Liouville和Geünwald Letnikov分数阶导数定义之间的联系,提出了3种数值解法来模拟其解析解.最后给出了数值例子,从而说明了所提出的3种数值方法可以用于模拟分数阶控制系统的性态.

Fractional-order mathematical models are applied in fractional-order dynamical controlled systems.These new models are more adequate than integer-order models.A four-term fractional differential equation corresponded by fractional-order controlled systems is considered.The existence and uniqueness of the solution of this model is given,and the analytical solution is described by Mittag-Leffle function.Using the relationship between the Caputo,Riemann-Liouville and Geünwald-Letnikov definitions,three numerical methods for the fractional-order control system are proposed.Finally,some numerical examples are presented.