We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (...We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.展开更多
By using the stochastic martingale theory, convergence properties of stochastic gradient （SG） identification algorithms are studied under weak conditions. The analysis indicates that the parameter estimates by the S...By using the stochastic martingale theory, convergence properties of stochastic gradient （SG） identification algorithms are studied under weak conditions. The analysis indicates that the parameter estimates by the SG algorithms consistently converge to the true parameters, as long as the information vector is persistently exciting （i.e., the data product moment matrix has a bounded condition number） and that the process noises are zero mean and uncorrelated. These results remove the strict assumptions, made in existing references, that the noise variances and high-order moments exist, and the processes are stationary and ergodic and the strong persis- tent excitation condition holds. This contribution greatly relaxes the convergence conditions of stochastic gradient algorithms. The simulation results with bounded and unbounded noise variances confirm the convergence conclusions proposed.展开更多
考虑有色噪声干扰的Hamm erste in非线性系统的辨识,通过梯度搜索原理推导了增广投影算法,简化增广投影算法和增广随机梯度辨识算法。基本思想是将增广信息向量中的未知噪声项用其估计残差代替。增广投影算法对噪声非常敏感,增广随机梯...考虑有色噪声干扰的Hamm erste in非线性系统的辨识,通过梯度搜索原理推导了增广投影算法,简化增广投影算法和增广随机梯度辨识算法。基本思想是将增广信息向量中的未知噪声项用其估计残差代替。增广投影算法对噪声非常敏感,增广随机梯度算法的收敛速度慢,为了解决这些不足,在增广随机梯度算法中引入遗忘因子,来改善参数估计精度,进一步通过仿真来比较算法的估计误差以及收敛速度。展开更多
文摘We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60574051 and 60674092) the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2007017) and by Program for Innovative Research Team of Jiangnan University
文摘By using the stochastic martingale theory, convergence properties of stochastic gradient （SG） identification algorithms are studied under weak conditions. The analysis indicates that the parameter estimates by the SG algorithms consistently converge to the true parameters, as long as the information vector is persistently exciting （i.e., the data product moment matrix has a bounded condition number） and that the process noises are zero mean and uncorrelated. These results remove the strict assumptions, made in existing references, that the noise variances and high-order moments exist, and the processes are stationary and ergodic and the strong persis- tent excitation condition holds. This contribution greatly relaxes the convergence conditions of stochastic gradient algorithms. The simulation results with bounded and unbounded noise variances confirm the convergence conclusions proposed.
文摘考虑有色噪声干扰的Hamm erste in非线性系统的辨识,通过梯度搜索原理推导了增广投影算法,简化增广投影算法和增广随机梯度辨识算法。基本思想是将增广信息向量中的未知噪声项用其估计残差代替。增广投影算法对噪声非常敏感,增广随机梯度算法的收敛速度慢,为了解决这些不足,在增广随机梯度算法中引入遗忘因子,来改善参数估计精度,进一步通过仿真来比较算法的估计误差以及收敛速度。
