直接加权优化辨识中未知权重值的迭代选取

Iterative selection of unknown weights in direct weight optimization identification

对于非线性系统的直接加权优化辨识算法,通过在原线性仿射函数形式中,增加若干关于输入观测数据序列的线性项来增强逼近非线性。对于增加若干线性项后展开式中的两类未知权重值的选取,分别从理论和实用上推导出这些未知权重值的选取过程,并明确权重值间的关键和辅助作用。理论上的推导分析可明确增加的未知权重值在整个逼近非线性系统的目的中起着辅助作用;实用上的推导分析展示了怎样将某些复杂的最优化问题经过整理变换成常见的最优化问题,从而可利用最基础的优化方法来求解,并分别对理论和实用算法的收敛性做了必要的证明。最后用仿真算例验证所提方法的有效性和可行性。

For the direct weighted optimization identification method for the nonlinear system, some linear terms about input measured date sequences in the former linear affine function are added to approximate the non- linear property. To select the two classes of unknown weights in the expression of the some more linear terms, the detailed process is derived on how to select these unknown weights from theory analysis and engineering practice respectively, and the key and auxiliary role between the unknown weights is made sure. From the theo- ry analysis, the added unknown weights＇ auxiliary role can be known in the whole process of approximating the nonlinear system. From the practice analysis, it shows how to transform some complex optimization problems into the corresponding common problems. Then the common problems can be solved by the basic optimization method. The convergences of the theory and practical are proved. Finally, the efficiency and possibility of the proposed strategy can be confirmed hy the simulation example results.