Identification of the gain system with quantized observations and bounded persistent excitations
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- 作者：Jin Guo (1)
YanLong Zhao (1) - 关键词：system identification ; quantized observation ; bounded persistent excitation ; binary ; valued output ; multi ; threshold quantization ; convergence ; convergence rate
- 刊名：SCIENCE CHINA Information Sciences
- 出版年：2014
- 出版时间：January 2014
- 年：2014
- 卷：57
- 期：1
- 页码：1-15
- 全文大小：430 KB
- 作者单位：Jin Guo (1)
YanLong Zhao (1)
1. Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China - ISSN：1869-1919
文摘
System identification with quantized observations and persistent excitations is a fundamental and difficult problem. As the first step, this paper takes the gain system for example to investigate the identification with quantized observations and bounded persistently exciting inputs. Firstly, the identification with single threshold quantization is considered. A projection recursive algorithm is proposed to estimate the unknown parameter. By use of the conditional expectation of quantized observations with respect to the estimates, the algorithm is shown to be both mean-square and almost surely convergent. The upper bound of the convergence rate is also obtained, which has the same order as the one of the optimal estimation in the case where the system output is exactly known. Secondly, for the multi-threshold quantization, the identification algorithm is similarly constructed and its asymptotic property is analyzed. Using a multi-linear transformation, the optimal scheme of quantization values and thresholds is given. A numerical example is simulated to demonstrate the effectiveness of the algorithms and the main results obtained.