基于改进的布谷鸟搜索算法对分数阶生物系统的参数估计（英文）

Parameter estimation of fractional dynamical models arising from biological systems using an improved cuckoo search algorithm

近年来,非线性分数阶系统的参数估计问题已经在许多科学和工程领域特别是计算生物学中,引起了广泛的兴趣.本文针对分数阶生物系统的参数估计问题,将系统参数和分数阶导数同时作为独立的未知参数来进行估计,并提出了一种改进的布谷鸟搜索(improved cuckoo search,ICS)算法来求解该问题.在ICS算法中,通过引入一个自适应参数控制机制,同时结合反向学习方法,从而达到提高算法收敛速度和估计值精度的目的.最后,以三种经典的分数阶生物动力系统模型为例进行了数值仿真,其中还考虑了有测量误差和噪声数据的情形.仿真结果表明ICS算法具有良好的适应性、较高的收敛可靠性及精度,为求解非线性分数阶系统参数估计问题提供了一种有效工具.

Recently,parameter estimation of nonlinear fractional-order systems has attracted great interest among many fields of science and engineering,especially computational biology.In this paper,we consider fractional dynamical models arising from biological systems,and parameter estimation of which is converted into a multi-dimensional optimization problem by treating both systematic parameters and fractional derivative orders as independent unknown parameters to be estimated.Moreover,an improved cuckoo search(ICS)algorithm is proposed as a novel technique to solve the problem of parameter estimation.In ICS,a simple adaptive parameter control mechanism is introduced,at the mean time,the opposition-based learning method is incorporated to the presented algorithm so that it can accelerate convergence speed and improve the accuracy of the estimated values.Numerical simulations are carried out on three typical fractional-order dynamical biological systems.We also investigate the condition with measurement error and noisy data.The simulation results demonstrate the effectiveness and efficiency of ICS,and show its significant superiority to the other methods.Thus,ICS may be deemed to be a promising tool for parameter estimation of nonlinear fractional-order systems.