智能优化算法对提高分数阶算子的有理逼近精度研究

Research on Intelligent Algorithm for Improving The Accuracy of Rational Function of Fractional Order Calculus Operators

针对分数阶微积分算子具有无限维特性而不能够直接数值实现,讨论了其有理函数逼近的优化问题.通过采用Oustaloup算法对分数阶微分算子进行有理函数逼近,确定其有理逼近传递函数结构.然后采用粒子群优化算法对该有理逼近传递函数的各系数进行再次寻优,实现提高分数阶微积分算子有理逼近精度的目的.仿真实例验证了所提方法的有效性.

For fractional calculus operators with the feature of infinite dimensional which is unable to realize the value directly, the optimization problem of the rational approximation function is discussed. Using Oustaloup algorithm for fractional operators to obtain rational approximation function, the structure of the rational transfer function is determined. Then PSO algorithm is used to seek for optimal coefficients of the transfer function in order to improve the accuracy of the rational function approximation for the fractional operators. Simulations demonstrate the effectiveness of the proposed method.