分数阶非线性时滞微分方程参数和阶的估计方法

Parameters and Order Estimation Methods of Fractional Nonlinear Delay Differential Equation

分数阶非线性时滞微分方程具有广泛的应用,因而根据部分观测值估计方程的参数和阶有重要意义。首先通过预估-校正法求出方程组的预测值,结合部分观测值建立优化目标函数,再采用鸡群算法给出最优参数和阶的估计值。通过计算机模拟,验证了方法的有效性。

Fractional-order delay nonlinear dynamics system is used more and more widely in science and engineering.Based on partial observed data,fitting the parameters and order plays an important role in practical problem.Given the guess values of parameters and order,the prediction values of differential equations＇ solutions can be computed by the predictor-corrector scheme algorithm,and the optimization objective function will be constructed by using difference between observed data and prediction values.So the optimal parameters and order are searched by chicken swarm optimization method.Finally,by computer simulation,the algorithm is proved valid.