Iterative Identification Algorithms for Bilinear-in-parameter Systems by Using the Over-parameterization Model and the Decomposition

다국어 초록 (Multilingual Abstract)

This paper focuses on the identification problem for a class of bilinear-in-parameter systems with an additive noise modeled by an autoregressive moving average process. By using the over-parameterization model, the special form of the bilinear term can be obtained by the model equivalent transformation. Then, we use a decomposition of the model into two synthetic models in order to separate the effect of the two sets of parameters, i.e., the coefficients of the nonlinear basis functions from the parameters of the colored noise. Moreover, two decomposition based iterative algorithms are proposed to identify the unknown parameters. A numerical example is presented to confirm the effectiveness of the proposed methods.

참고문헌 (Reference)

1 H. L. Gao, "The perturbed sparre Andersen model with a threshold dividend strategy" 220 (220): 394-408, 2008

2 C. C. Yin, "The perturbed compound Poisson risk process with investment and debit interest" 12 (12): 391-413, 2010

3 L. Xu, "The parameter estimation algorithms for dynamical response signals based on the multiinnovation theory and the hierarchical principle" 11 (11): 228-237, 2017

4 L. Xu, "The parameter estimation algorithms based on the dynamical response measurement data" 9 (9): 1-12, 2017

5 M. H. Li, "The least squares based iterative algorithms for parameter estimation of a bilinear system with autoregressive noise using the data filtering technique" 147 : 23-34, 2018

6 X. F. Li, "Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls" 100 : 24-30, 2017

7 P. Li, "Storage aided system property enhancing and hybrid robust smoothing for large-scale PV systems" 8 (8): 2871-2879, 2017

8 X. Zhang, "State filteringbased least squares parameter estimation for bilinear systems using the hierarchical identification principle" 12 (12): 1704-1713, 2018

9 Y. Cao, "Standard analysis for transfer delay in CTCS-3" 26 (26): 1057-1063, 2017

10 Y. Y. Wang, "Sliding mode control of fuzzy singularly perturbed systems with application to electric circuit" 2017

11 F. Liu, "Singular integrals related to homogeneous mappings in triebel-lizorkin spaces" 11 (11): 1075-1097, 2017

12 Y. Y. Wang, "SMC design for robust stabilization of nonlinear Markovian jump singular systems" 63 (63): 219-224, 2018

13 F. Liu, "Rough maximal singular integral and maximal operators supported by subvarieties on Triebel-Lizorkin spaces" 171 : 41-72, 2018

14 Zheheng Rao, "Research on a handwritten character recognition algorithm based on an extended nonlinear kernel residual network" 한국인터넷정보학회 12 (12): 413-435, 2018

15 F. Liu, "Regularity of discrete multisublinear fractional maximal functions" 60 (60): 1461-1476, 2017

16 X. Zhang, "Recursive parameter identification of the dynamical models for bilinear state space systems" 89 (89): 2415-2429, 2017

17 L. Xu, "Recursive least squares and multiinnovation stochastic gradient parameter estimation methods for signal modeling" 36 (36): 1735-1753, 2017

18 J. L. Ding, "Recursive and iterative least squares parameter estimation algorithms for multiple-input-output-error systems with autoregressive noise" 37 (37): 1884-1906, 2018

19 F. Ding, "Performance analysis of the generalised projection identification for time-varying systems" 10 (10): 2506-2514, 2016

20 Ling Xu, "Parameter Estimation for Control Systems based on Impulse Responses" 제어·로봇·시스템학회 15 (15): 2471-2479, 2017

21 Y. Cao, "Parallel processing algorithm for railway signal fault diagnosis data based on cloud computing" 88 : 279-283, 2018

22 Y. Z. Zhang, "Optimization of information interaction protocols in cooperative vehicle-infrastructure systems" 27 (27): 439-444, 2018

23 C. C. Yin, "Optimality of the threshold dividend strategy for the compound Poisson model" 81 (81): 1841-1846, 2011

24 C. C. Yin, "Optimal dividend problem with a terminal value for spectrally positive Levy processes" 53 (53): 769-773, 2013

25 F. Liu, "On the triebel-lizorkin space boundedness of marcinkiewicz integrals along compound surfaces" 20 (20): 515-535, 2017

26 F. Liu, "On the regularity of maximal operators supported by submanifolds" 453 (453): 144-158, 2017

27 M. Gan, "On some separated algorithms for separable nonlinear squares problems" 2018

28 C. C. Yin, "Nonexponential asymptotics for the solutions of renewal equations, with applications" 43 (43): 815-824, 2008

29 Ali Zribi, "Multiple Model Reduction Approach using Gap Metric and Stability Margin for Control Nonlinear Systems" 제어·로봇·시스템학회 15 (15): 267-273, 2017

30 P. Li, "Multi-objective sizing optimization for island microgrids using triangular aggregation model and Levy-Harmony algorithm" 14 (14): 3495-3505, 2018

31 N. Zhao, "Monitoring strategy for relay incentive mechanism in cooperative communication networks" 60 : 14-29, 2017

32 Dong-Qing Wang, "Maximum likelihood estimation method for dual-rate Hammerstein systems" 제어·로봇·시스템학회 15 (15): 698-705, 2017

33 Feng Ding, "Least Squares based Iterative Parameter Estimation Algorithm for Stochastic Dynamical Systems with ARMA Noise Using the Model Equivalence" 제어·로봇·시스템학회 16 (16): 630-639, 2018

34 F. Ding, "Iterative parameter identification for pseudo-linear systems with ARMA noise using the filtering technique" 12 (12): 892-899, 2018

35 L. Xu, "Iterative parameter estimation for signal models based on measured data" 37 (37): 3046-3069, 2018

36 M. T. Chen, "Iterative identification algorithms for bilinear-in-parameter systems with autoregressive moving average noise" 354 (354): 7885-7898, 2017

37 F. Ding, "Hierarchical stochastic gradient algorithm and its performance analysis for a class of bilinear-in-parameter systems" 36 (36): 1393-1405, 2017

38 Ling Xu, "Hierarchical Parameter Estimation for the Frequency Response Based on the Dynamical Window Data" 제어·로봇·시스템학회 16 (16): 1756-1764, 2018

39 Kaihong Yang, "Hierarchical Control for Nonlinear Systems by Partial-state Feedback" 제어·로봇·시스템학회 15 (15): 595-602, 2017

40 Junyong Zhai, "Global Finite-time Stabilization for a Class of Switched Nonlinear Systems via Output Feedback" 제어·로봇·시스템학회 15 (15): 1975-1982, 2017

41 C. C. Yin, "Exit problems for jump processes with applications to dividend problems" 245 : 30-52, 2013

42 Y. Y. Wang, "Dissipativity-based fuzzy integral sliding mode control of continuous-time T-S fuzzy systems" 26 (26): 1164-1176, 2017

43 P. Ma, "Decomposition-based recursive least squares identification methods for multivariate pseudolinear systems using the multi-innovation" 49 (49): 920-928, 2018

44 F. Liu, "Continuity and approximate differentiability of multisublinear fractional maximal functions" 21 (21): 25-40, 2018

45 X. Zhang, "Combined state and parameter estimation for a bilinear state space system with moving average noise" 355 (355): 3079-3103, 2018

46 D. Q. Zhu, "Biologically inspired self-organizing map applied to task assignment and path planning of an AUV system" 10 (10): 304-313, 2018

47 M. Gan, "A variable projection approach for efficient estimation of RBF-ARX model" 45 (45): 462-471, 2015

48 F. Ding, "A recursive least squares parameter estimation algorithm for output nonlinear autoregressive systems using the inputoutput data filtering" 354 (354): 6938-6955, 2017

49 L. Xu, "A multiinnovation state and parameter estimation algorithm for a state space system with d-step state-delay" 140 : 97-103, 2017

50 F. Ding, "A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation" 355 (355): 3737-3752, 2018

51 Y. J. Wang, "A filtering based multi-innovation gradient estimation algorithm and performance analysis for nonlinear dynamical systems" 82 (82): 1171-1191, 2017

52 E. W. Bai, "A blind approach to the Hammerstein-Wiener model identification" 38 : 967-979, 2002