scholarly journals Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 428 ◽  
Author(s):  
Feng Ding ◽  
Jian Pan ◽  
Ahmed Alsaedi ◽  
Tasawar Hayat
Keyword(s):  
Iterative Algorithm ◽  
System Analysis ◽  
Stochastic Systems ◽  
Controller Design ◽  
Observation Data ◽  
Identification Problems ◽  
Estimation Algorithms ◽  
Gradient Based ◽  
Parameter Identification Problems ◽  
Identification Theory

It is well-known that mathematical models are the basis for system analysis and controller design. This paper considers the parameter identification problems of stochastic systems by the controlled autoregressive model. A gradient-based iterative algorithm is derived from observation data by using the gradient search. By using the multi-innovation identification theory, we propose a multi-innovation gradient-based iterative algorithm to improve the performance of the algorithm. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms.

Two-stage gradient-based iterative algorithm for bilinear stochastic systems over the moving data window

2020 ◽  
Vol 357 (15) ◽  
pp. 11021-11041
Author(s):  
Siyu Liu ◽  
Li Xie ◽  
Ling Xu ◽  
Feng Ding ◽  
Ahmed Alsaedi ◽  
...  
Keyword(s):  
Iterative Algorithm ◽  
Stochastic Systems ◽  
Two Stage ◽  
Data Window ◽  
Gradient Based

scholarly journals Least-Squares Based and Gradient Based Iterative Parameter Estimation Algorithms for a Class of Linear-in-Parameters Multiple-Input Single-Output Output Error Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Cheng Wang ◽  
Tao Tang ◽  
Dewang Chen
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Iterative Algorithm ◽  
Parameter Estimates ◽  
Iterative Search ◽  
Estimation Algorithms ◽  
Single Output ◽  
Multiple Input ◽  
Gradient Based ◽  
Simulation Results

The identification of a class of linear-in-parameters multiple-input single-output systems is considered. By using the iterative search, a least-squares based iterative algorithm and a gradient based iterative algorithm are proposed. A nonlinear example is used to verify the effectiveness of the algorithms, and the simulation results show that the least-squares based iterative algorithm can produce more accurate parameter estimates than the gradient based iterative algorithm.

Parameter Estimation Algorithms for Hammerstein–Wiener Systems With Autoregressive Moving Average Noise

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Yanjiao Wang ◽  
Feng Ding
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Data Filtering ◽  
Estimation Algorithms ◽  
Gradient Based ◽  
Wiener Systems ◽  
Filtering Technique ◽  
Identification Theory

Hammerstein–Wiener (H–W) systems are a class of typical nonlinear systems. This paper studies the gradient-based parameter estimation algorithms for H–W nonlinear systems based on the multi-innovation identification theory and the data filtering technique. The proposed methods include a generalized extended stochastic gradient (GESG) algorithm, a multi-innovation GESG (MI-GESG) algorithm, a data filtering based GESG (F-GESG) algorithm and a data filtering based MI-GESG algorithm. Finally, the computational efficiency of the proposed algorithms are analyzed and compared. The simulation example verifies the theoretical results.

scholarly journals Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang ◽  
Po-Hsun Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ship Steering

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

Feasible Controller Design for Stochastic Systems

1997 ◽  
Vol 20 (3) ◽  
pp. 535-541 ◽  
Author(s):  
C. Frangos ◽  
Y. Yavin
Keyword(s):  
Stochastic Systems ◽  
Controller Design

scholarly journals The optimal convergence factor of the gradient based iterative algorithm for linear matrix equations

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 607-613 ◽  
Author(s):  
Xiang Wang ◽  
Dan Liao
Keyword(s):  
Iterative Algorithm ◽  
Numerical Experiments ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Convergence Factor ◽  
Gradient Based ◽  
Gradient Type ◽  
And Mathematics ◽  
Computers And Mathematics ◽  
Linear Matrix Equations

A hierarchical gradient based iterative algorithm of [L. Xie et al., Computers and Mathematics with Applications 58 (2009) 1441-1448] has been presented for finding the numerical solution for general linear matrix equations, and the convergent factor has been discussed by numerical experiments. However, they pointed out that how to choose a best convergence factor is still a project to be studied. In this paper, we discussed the optimal convergent factor for the gradient based iterative algorithm and obtained the optimal convergent factor. Moreover, the theoretical results of this paper can be extended to other methods of gradient-type based. Results of numerical experiments are consistent with the theoretical findings.

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