With the advent of tensor-valued time series data,tensor autoregression appears in many fields,in which the coefficient estimation is confronted with the problem of dimensional disaster.Based on the tensor ring(TR)dec...With the advent of tensor-valued time series data,tensor autoregression appears in many fields,in which the coefficient estimation is confronted with the problem of dimensional disaster.Based on the tensor ring(TR)decomposition,an autoregression model with one order for tensor-valued responses is proposed in this paper.A randomized method,TensorSketch,is applied to the TR autoregression model for estimating the coefficient tensor.Convergence and some properties of the proposed methods are given.Finally,some numerical experiment results on synthetic data and real data are given to illustrate the effectiveness of the proposed method.展开更多
We investigate the identification problems of a class of linear stochastic time-delay systems with unknown delayed states in this study. A time-delay system is expressed as a delay differential equation with a single ...We investigate the identification problems of a class of linear stochastic time-delay systems with unknown delayed states in this study. A time-delay system is expressed as a delay differential equation with a single delay in the state vector. We first derive an equivalent linear time-invariant(LTI) system for the time-delay system using a state augmentation technique. Then a conventional subspace identification method is used to estimate augmented system matrices and Kalman state sequences up to a similarity transformation. To obtain a state-space model for the time-delay system, an alternate convex search(ACS) algorithm is presented to find a similarity transformation that takes the identified augmented system back to a form so that the time-delay system can be recovered. Finally, we reconstruct the Kalman state sequences based on the similarity transformation. The time-delay system matrices under the same state-space basis can be recovered from the Kalman state sequences and input-output data by solving two least squares problems. Numerical examples are to show the effectiveness of the proposed method.展开更多
基金the handling editor and anonymous referees for useful comments and suggestions which contribute to improving the quality of the manuscriptcrossing research project of Shanghai University of Engineering Science(No.SL-O01).
文摘With the advent of tensor-valued time series data,tensor autoregression appears in many fields,in which the coefficient estimation is confronted with the problem of dimensional disaster.Based on the tensor ring(TR)decomposition,an autoregression model with one order for tensor-valued responses is proposed in this paper.A randomized method,TensorSketch,is applied to the TR autoregression model for estimating the coefficient tensor.Convergence and some properties of the proposed methods are given.Finally,some numerical experiment results on synthetic data and real data are given to illustrate the effectiveness of the proposed method.
文摘We investigate the identification problems of a class of linear stochastic time-delay systems with unknown delayed states in this study. A time-delay system is expressed as a delay differential equation with a single delay in the state vector. We first derive an equivalent linear time-invariant(LTI) system for the time-delay system using a state augmentation technique. Then a conventional subspace identification method is used to estimate augmented system matrices and Kalman state sequences up to a similarity transformation. To obtain a state-space model for the time-delay system, an alternate convex search(ACS) algorithm is presented to find a similarity transformation that takes the identified augmented system back to a form so that the time-delay system can be recovered. Finally, we reconstruct the Kalman state sequences based on the similarity transformation. The time-delay system matrices under the same state-space basis can be recovered from the Kalman state sequences and input-output data by solving two least squares problems. Numerical examples are to show the effectiveness of the proposed method.
