Identification of the gain system with quantized observations and bounded persistent excitations  

作　　者：GUO Jin ZHAO YanLong 

机构地区：[1]Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science,Chinese Academy of Sciences

出　　处：《Science China(Information Sciences)》2014年第1期213-227,共15页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.61174042);Youth Innovation Promotion Association of Chinese Academy of Sciences(Grant No.4106960)

摘　　要：System identification with quantized observations and persistent excitations is a fundamental and difcult 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 efectiveness of the algorithms and the main results obtained.System identification with quantized observations and persistent excitations is a fundamental and difcult 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 efectiveness of the algorithms and the main results obtained.

关 键 词：system identification quantized observation bounded persistent excitation binary-valued output multi-threshold quantization convergence convergence rate 

分 类 号：O231[理学—运筹学与控制论]