非线性离散系统的伴随辨识法

Adjoint identification approach for nonlinear discrete systems

中文关键词  离散非线性系统  差分方程  伴随向量  拟牛顿信赖域方法

英文关键词  discrete nonlinear system  difference equation  adjoint vector  Quasi_Newton trust region method

中文摘要

      对非线性离散系统辨识的研究,通常是将其转化成一个非线性优化问题.为此需要计算目标函数对参数向量的梯度,以往的方法需要求解一个矩阵差分方程,计算量颇大.依据系统输出量测值来确定含在系统中的未知参数向量,首先引进伴随状态向量,代替矩阵差分方程求解的是计算一个向量差分方程,从而大大简化计算,然后将这种梯度计算方法结合进拟牛顿信赖域法中.最后给出了应用此方法的一个实际例子,数值仿真的结果说明方法是有效的.

英文摘要

      The usual identification approach to nonlinear discrete systems is to use nonlinear optimization methods to estimate the parameter vector.Thus,the gradient of a cost functional with respect to the parameter vector must be computed and then a first order matrix difference equation should be solved with the commonly used methods.The discrete_time system considered in the paper is described by a first order vector difference equation.One of the identification objects is to estimate unknown parameter vector contained in the system based on the measurement outputs of the system.First,a first order vector difference equation was solved to reduce the computational load after introducing an adjoint vector.Then,an algorithm was presented combining the adjoint identification approach with a Quasi_Newton trust region algorithm,which is a global convergence Quasi_Newton method.Finally,an example was given to illustrate the effectiveness of this method.