| 引用本文: | 李银国,汤卓群,黄 镭.非持续激励条件下系统辨识递推最小二乘最小范数算法[J].控制理论与应用,2009,26(4):365~370.[点击复制] |
| LI Yin-guo,TANG Zhuo-qun,HUANG Lei.Recursive least-squares and minimum-norm algorithm for system identification without persistent excitation condition[J].Control Theory and Technology,2009,26(4):365~370.[点击复制] |
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| 非持续激励条件下系统辨识递推最小二乘最小范数算法 |
| Recursive least-squares and minimum-norm algorithm for system identification without persistent excitation condition |
| 摘要点击 1916 全文点击 1457 投稿时间：2007-09-11 修订日期：2008-10-31 |
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| DOI编号 |
| 2009,26(4):365-370 |
| 中文关键词 系统辨识 最小二乘算法 持续激励条件 最小二乘最小范数解 |
| 英文关键词 system identification least square algorithm persistent excitation conditions recursive least-square and minimum-norm algorithm |
| 基金项目 国家863计划资助课题(2006AA11A1C1-3); 国家973计划前期研究专项资助课题(2008CB317111). |
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| 中文摘要 |
| 系统辨识中广泛应用的最小二乘算法需要输入向量序列满足持续激励性条件(PE条件); 但在大多情况下这是难以满足的. 本文提出了一种不依赖于PE条件的递推最小二乘、最小范数辨识算法. 首先分析了最小二乘算法解空间的结构, 并运用罚函数方法, 将参数辨识问题转化为无约束优化问题. 然后, 提出了将步长、罚因子等过程控制参数统一的迭代－递推形式的辨识算法, 证明了算法在给定的控制参数约束下收敛于唯一的最小二乘、最小范数解向量. 仿真实验表明在非PE条件下算法的有效性. |
| 英文摘要 |
| The widely used least-squares algorithms for system identification rely on the assumption that the sequence of input vectors satisfies the persistent excitation conditions (PE conditions); however, this condition is difficult to be realized in most cases. For this purpose, a recursive least-squares and minimum-norm (RLS–MN) identification algorithm that does not depend upon PE conditions is proposed. First, the structure of the solution space of the least squares algorithm is analyzed and the parameter identification problem is converted to an unconstraint optimization problem by using the penalty function method; and then, an iteration-recursion-based identification algorithm is presented by unifying the process control parameters, such as step width and penalty factor. This algorithm is proved to converge to a unique least-squares and minimum-norm solution vector when the control parameters satisfy the given constraint conditions. Finally, simulation results are presented to confirm the validity of the algorithm without using PE conditions. |
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