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
This paper investigates the problem of seeking minimum of API (Auxiliary Performance Index) in parameters of Data Model instead of parameters of Adaptive Filter in order to avoid the phenomenon of over parameterizatio...This paper investigates the problem of seeking minimum of API (Auxiliary Performance Index) in parameters of Data Model instead of parameters of Adaptive Filter in order to avoid the phenomenon of over parameterization. This problem was stated by Semushin in [2]. The solution to the problem can be considered as the development of API approach to parameter identification in stochastic dynamic systems.展开更多
This paper surveys the field of adaptation in stochastic systems as it has developed over the last four decades. The author’s research in this field is summarized and a novel solution for fitting an adaptive model in...This paper surveys the field of adaptation in stochastic systems as it has developed over the last four decades. The author’s research in this field is summarized and a novel solution for fitting an adaptive model in state space (instead of response space) is given.展开更多
This paper surveys the field of adaptation mechanism design for uncertainty parameter estimation as it has developed over the last four decades. The adaptation mechanism under consideration generally serves two tightl...This paper surveys the field of adaptation mechanism design for uncertainty parameter estimation as it has developed over the last four decades. The adaptation mechanism under consideration generally serves two tightly coupled functions: model identification and change point detection. After a brief introduction, the pa-per discusses the generalized principles of adaptation based both on the engineering and statistical literature. The stochastic multiinput multioutput (MIMO) system under consideration is mathematically described and the problem statement is given, followed by a definition of the active adaptation principle. The distinctive property of the principle as compared with the Minimum Prediction Error approach is outlined, and a plan for a more detailed exposition to be provided in forthcoming papers is given.展开更多
In this work,an efficient sample-wise data driven control solver will be developed to solve the stochastic optimal control problem with unknown model parameters.A direct filter method will be applied as an online para...In this work,an efficient sample-wise data driven control solver will be developed to solve the stochastic optimal control problem with unknown model parameters.A direct filter method will be applied as an online parameter estimation method that dynamically estimates the target model parameters upon receiving the data,and a sample-wise optimal control solver will be provided to efficiently search for the optimal control.Then,an effective overarching algorithm will be introduced to combine the parameter estimator and the optimal control solver.Numerical experiments will be carried out to demonstrate the effectiveness and the efficiency of the sample-wise data driven control method.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.
文摘This paper investigates the problem of seeking minimum of API (Auxiliary Performance Index) in parameters of Data Model instead of parameters of Adaptive Filter in order to avoid the phenomenon of over parameterization. This problem was stated by Semushin in [2]. The solution to the problem can be considered as the development of API approach to parameter identification in stochastic dynamic systems.
文摘This paper surveys the field of adaptation in stochastic systems as it has developed over the last four decades. The author’s research in this field is summarized and a novel solution for fitting an adaptive model in state space (instead of response space) is given.
文摘This paper surveys the field of adaptation mechanism design for uncertainty parameter estimation as it has developed over the last four decades. The adaptation mechanism under consideration generally serves two tightly coupled functions: model identification and change point detection. After a brief introduction, the pa-per discusses the generalized principles of adaptation based both on the engineering and statistical literature. The stochastic multiinput multioutput (MIMO) system under consideration is mathematically described and the problem statement is given, followed by a definition of the active adaptation principle. The distinctive property of the principle as compared with the Minimum Prediction Error approach is outlined, and a plan for a more detailed exposition to be provided in forthcoming papers is given.
基金partially supported by U.S.Department of Energy through FASTMath Institute and Office of Science,Advanced Scientific Computing Research program under the grant DE-SC0022297the support from U.S.National Science Foundation through project DMS-2142672.
文摘In this work,an efficient sample-wise data driven control solver will be developed to solve the stochastic optimal control problem with unknown model parameters.A direct filter method will be applied as an online parameter estimation method that dynamically estimates the target model parameters upon receiving the data,and a sample-wise optimal control solver will be provided to efficiently search for the optimal control.Then,an effective overarching algorithm will be introduced to combine the parameter estimator and the optimal control solver.Numerical experiments will be carried out to demonstrate the effectiveness and the efficiency of the sample-wise data driven control method.
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。
