This paper is concerned with the optimal and suboptimal deconvolution problems for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time stamped, the random delayed ...This paper is concerned with the optimal and suboptimal deconvolution problems for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time stamped, the random delayed system is reconstructed as an equivalent delay-free one by using measurement reorganization technique, and then an optimal input white noise estimator is presented based on the stochastic Kahnan filtering theory. However, tb_e optimal white-noise estimator is timevarying, stochastic, and doesn＇t converge to a steady state in general. Then an alternative suboptimal input white-noise estimator with deterministic gains is developed under a new criteria. The estimator gain and its respective error covariance-matrix information are derived based on a new suboptimal state estimator. It can be shown that the suboptimal input white-noise estimator converges to a steady-state one under appropriate assumptions.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supported by the National Nature Science Foundation of China under Grant Nos.61104050,61203029the Natural Science Foundation of Shandong Province under Grant No.ZR2011FQ020+2 种基金the Scientific Research Foundation for Outstanding Young Scientists of Shandong Province under Grant No.BS2013DX008the Graduate Education Innovation Project of Shandong Province under Grant No.SDYC12006the Ph.D.Foundation Program of University of Jinan under Grant No.XBS1044
文摘This paper is concerned with the optimal and suboptimal deconvolution problems for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time stamped, the random delayed system is reconstructed as an equivalent delay-free one by using measurement reorganization technique, and then an optimal input white noise estimator is presented based on the stochastic Kahnan filtering theory. However, tb_e optimal white-noise estimator is timevarying, stochastic, and doesn＇t converge to a steady state in general. Then an alternative suboptimal input white-noise estimator with deterministic gains is developed under a new criteria. The estimator gain and its respective error covariance-matrix information are derived based on a new suboptimal state estimator. It can be shown that the suboptimal input white-noise estimator converges to a steady-state one under appropriate assumptions.
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.
