Convergence analysis of estimation algorithms for dual-rate stochastic systems
Convergence analysis of estimation algorithms for dual-rate stochastic systems
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DOI：
10.1016/j.amc.2005.09.048
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发表时间：
2006-05
期刊：
影响因子：
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通讯作者：
F. Ding;P. X. Liu;Yang Shi
中科院分区：
文献类型：
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作者：
F. Ding;P. X. Liu;Yang Shi
辨识是利用测量的输入输出数据{u(T)，y(T)}估计系统的未知参数。现有的辨识方法大多假定输入-输出{u(T)，y(T)}在每个采样时刻t可用。本文研究一类双速率采样数据系统，其中所有输入u(T)都可用，但只有稀有输出{y(Qt)}可用(q>；1为整数)。利用多项式变换技术建立了这类双速率系统的数学模型，提出了直接利用双速率输入输出数据{u(T)，y(Qt)}进行参数辨识和样本间输出估计的新算法，并利用随机过程理论和随机鞅理论详细研究了算法在随机框架下的收敛性质。证明了：(1)在持续激励条件下，参数估计误差一致收敛于零；(2)样本间输出估计误差一致有界。最后，我们以一个实验水位系统为例，对提出的算法进行了说明和测试。
Identification is to estimate the unknown parameters of systems by using the measured input–output data {u(t),y(t)}. Most existing identification approaches assume that the input–output {u(t),y(t)} is available at each sampling instant t. This paper focuses on a class of dual-rate sampled-data systems in which all inputs u(t) are available, but only scarce outputs {y(qt)} are available (q>1 being an integer). We derive a mathematical model for such dual-rate systems by using a polynomial transformation technique, and present new algorithms for parameter identification and intersample output estimation using directly the dual-rate input–output data {u(t),y(qt)}, and study in detail convergence properties of the algorithms in the stochastic framework by using the stochastic process theory and stochastic martingale theory. We show that (1) the parameter estimation error consistently converges to zero under the persistent excitation condition; (2) the intersample output estimation error is uniformly bounded. Finally, we illustrate and test the proposed algorithms with example systems, including an experimental water-level system.