Data filtering based maximum likelihood extended gradient method for multivariable systems with autoregressive moving average noise     

Feiyan Chen  Feng Ding  Ling Xu  Tasawar Hayat 《Journal of The Franklin Institute》2018,355(7):3381-3398

For multivariable systems with autoregressive moving average noises, we decompose the multivariable system into m subsystems (m denotes the number of outputs) and present a maximum likelihood generalized extended gradient algorithm and a data filtering based maximum likelihood extended gradient algorithm to estimate the parameter vectors of these subsystems. By combining the maximum likelihood principle and the data filtering technique, the proposed algorithms are effective and have computational advantages over existing estimation algorithms. Finally, a numerical simulation example is given to support the developed methods and to show their effectiveness.  相似文献   

A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation     

Feng Ding  Huibo Chen  Ling Xu  Jiyang Dai  Qishen Li  Tasawar Hayat 《Journal of The Franklin Institute》2018,355(8):3737-3752

Mathematical models are basic for designing controller and system identification is the theory and methods for establishing the mathematical models of practical systems. This paper considers the parameter identification for Hammerstein controlled autoregressive systems. Using the key term separation technique to express the system output as a linear combination of the system parameters, the system is decomposed into several subsystems with fewer variables, and then a hierarchical least squares (HLS) algorithm is developed for estimating all parameters involving in the subsystems. The HLS algorithm requires less computation than the recursive least squares algorithm. The computational efficiency comparison and simulation results both confirm the effectiveness of the proposed algorithms.  相似文献   

Maximum likelihood recursive least squares estimation for multivariate equation-error ARMA systems     

Lijuan Liu  Yan Wang  Cheng Wang  Feng Ding  Tasawar Hayat 《Journal of The Franklin Institute》2018,355(15):7609-7625

This paper focuses on the parameter estimation problems of multivariate equation-error systems. A recursive generalized extended least squares algorithm is presented as a comparison. Based on the maximum likelihood principle and the coupling identification concept, the multivariate equation-error system is decomposed into several regressive identification models, each of which has only a parameter vector, and a coupled subsystem maximum likelihood recursive least squares identification algorithm is developed for estimating the parameter vectors of these submodels. The simulation example shows that the proposed algorithm is effective and has high estimation accuracy.  相似文献   

Auxiliary model based recursive generalized least squares identification algorithm for multivariate output-error autoregressive systems using the decomposition technique     

Qinyao Liu  Feng Ding  Yan Wang  Cheng Wang  Tasawar Hayat 《Journal of The Franklin Institute》2018,355(15):7643-7663

This paper focuses on the parameter estimation problem of multivariate output-error autoregressive systems. Based on the decomposition technique and the auxiliary model identification idea, we derive a decomposition based auxiliary model recursive generalized least squares algorithm. The key is to divide the system into two fictitious subsystems, the one including a parameter vector and the other including a parameter matrix, and to estimate the two subsystems using the recursive least squares method, respectively. Compared with the auxiliary model based recursive generalized least squares algorithm, the proposed algorithm has less computational burden. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithms.  相似文献   

Stationary distribution and extinction of a stochastic predator–prey model with herd behavior     

Qun Liu  Daqing Jiang  Tasawar Hayat  Ahmed Alsaedi 《Journal of The Franklin Institute》2018,355(16):8177-8193

In this paper, we propose and study a stochastic predator–prey model with herd behavior. Firstly, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the predator population in two cases, that is, the first case is the prey population survival and the predator population extinction; the second case is all the prey and predator populations extinction. Finally, some examples together with numerical simulations are introduced to illustrate the theoretical results.  相似文献   

Stationary distribution and extinction of a stochastic dengue epidemic model     

Qun Liu  Daqing Jiang  Tasawar Hayat  Ahmed Alsaedi 《Journal of The Franklin Institute》2018,355(17):8891-8914

In this paper, we investigate the dynamical behavior of a stochastic dengue epidemic model. First of all, by constructing a suitable stochastic Lyapunov function, we obtain sufficient conditions for the existence of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the diseases. The existence of stationary distribution implies stochastic weak stability.  相似文献   

Filtering based parameter estimation for observer canonical state space systems with colored noise     

Xuehai Wang  Feng Ding  Ahmed Alsaedi  Tasawar Hayat 《Journal of The Franklin Institute》2017,354(1):593-609

This paper surveys the identification of observer canonical state space systems affected by colored noise. By means of the filtering technique, a filtering based recursive generalized extended least squares algorithm is proposed for enhancing the parameter identification accuracy. To ease the computational burden, the filtered regressive model is separated into two fictitious sub-models, and then a filtering based two-stage recursive generalized extended least squares algorithm is developed on the basis of the hierarchical identification. The stochastic martingale theory is applied to analyze the convergence of the proposed algorithms. An experimental example is provided to validate the proposed algorithms.  相似文献   

Gradient-based iterative identification method for multivariate equation-error autoregressive moving average systems using the decomposition technique     

Zhengwei Ge  Feng Ding  Ling Xu  Ahmed Alsaedi  Tasawar Hayat 《Journal of The Franklin Institute》2019,356(3):1658-1676

This paper studies the parameter estimation problems of multivariate equation-error autoregressive moving average systems. Firstly, a gradient-based iterative algorithm is presented as a comparison. In order to improve the computational efficiency and the parameter estimation accuracy, a decomposition-based gradient iterative algorithm is presented by using the decomposition technique. The key is to transform an original system into two subsystems and to estimate the parameters of each subsystem, respectively. Compared with the gradient-based iterative algorithm, the decomposition-based algorithm requires less computational efforts, and the simulation results indicate that this algorithm is effective.  相似文献   

Dynamical behavior of stochastic multigroup S-DI-A epidemic models for the transmission of HIV     

Qun Liu  Daqing Jiang  Tasawar Hayat  Ahmed Alsaedi 《Journal of The Franklin Institute》2018,355(13):5830-5865

In this paper, we study two stochastic multigroup S-DI-A epidemic models for the transmission of HIV. For the stochastic S-DI-A epidemic model with periodic coefficients, we first obtain sufficient conditions for persistence in the mean of the disease. Then in the case of persistence, we show that the model admits a positive T-periodic solution by using Khasminskii theory of periodic solution. Moreover, we establish sufficient conditions for exponential extinction of the infectious disease. For the stochastic S-DI-A epidemic model disturbed by both white and telegraph noises, we first establish sufficient conditions for persistence in the mean of the disease. Then in the case of persistence, we obtain sufficient conditions for the existence of a unique ergodic stationary distribution of the positive solutions by constructing a suitable stochastic Lyapunov function with regime switching and we also obtain sufficient conditions for exponential extinction of the system with regime switching.  相似文献