【摘要】 给出了分数阶线性系统的一种有效辨识算法。该算法可以辨识出系统的模型参数,同时也可以对系统的阶次进行辨识。通过基底变换把分数阶系统的系统矩阵变换成对角阵,这就把原系统的输入、输出关系转化为若干简单的子系统的和,从而降低了辨识问题的复杂性。该算法还能容易地获得系统的输出误差对其模型参数及系统阶次的偏导数,从而可以选择利用梯度的优化算法,如梯度下降法和拟牛顿法等,进行系统辨识。最后给出了实例证明了算法的有效性。更多还原

【Abstract】 An efficient identification algorithm is given for fractional order systems. This algorithm can identify not only modal coefficients of the system, but also its differential order at the same time. The basic idea of the algorithm is to change the system matrix into a diagonal one by means of basis transform. This makes it possible to turn the system’s input-output relationship into the summation of several simple subsystems, and then identifications con be performed for these subsystes, and at lost the algebraic equivalent system of the original system con be obtained. The identification complexity is reduced. Another advantage of making this transform is that it is easier to obtain the partial derivatives of the output error with respect to both the modal coefficients and the system’s order. For this reason, optimization algorithms using gradient, such as gradient descent method and quasi-Newton method, can be used for system identification. An example is given to verify the effectiveness of this method.更多还原