Hierarchical gradient- and least squares-based iterative algorithms for input nonlinear output-error systems using the key term separation

Ding, Feng; Ma, Hao; Pan, Jian; Yang, Erfu

doi:10.1016/j.jfranklin.2021.04.006

Cited by 109 publications

(67 citation statements)

References 99 publications

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“…where u(k) ∈ R is the input of the system and u(k) = 0 for k ⩽ 0. Recently, a recursive least squares and a hierarchical least squares identification algorithms have been proposed for feedback nonlinear equation-error systems in (1)- (3). 36 This article studies the convergence of the recursive least squares parameter estimation algorithm for feedback nonlinear equation-error systems.…”

Section: System Descriptionmentioning

confidence: 99%

“…System identification is an important tool to construct the mathematical models from the observed data. [1][2][3][4][5] The accurate mathematical models are the basis of the implementation of the control strategies. [6][7][8][9] In the area of system identification, much attention has been concentrated on linear systems, nonlinear systems, bilinear systems and so on.…”

Section: Introductionmentioning

confidence: 99%

“…System identification is an important tool to construct the mathematical models from the observed data 1‐5 . The accurate mathematical models are the basis of the implementation of the control strategies 6‐9 .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Overall recursive least squares and overall stochastic gradient algorithms and their convergence for feedback nonlinear controlled autoregressive systems

Wei

Xiao

et al. 2022

Intl J Robust & Nonlinear

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This article deals with the problems of the parameter estimation for feedback nonlinear controlled autoregressive systems (i.e., feedback nonlinear equation‐error systems). The bilinear‐in‐parameter identification model is formulated to describe the feedback nonlinear system. An overall recursive least squares algorithm is developed to handle the difficulty of the bilinear‐in‐parameter. For the purpose of avoiding the heavy computational burden, an overall stochastic gradient algorithm is deduced and the forgetting factor is introduced to improve the convergence rate. Furthermore, the convergence analysis of the proposed algorithms are established by means of the stochastic process theory. The effectiveness of the proposed algorithms are illustrated by the simulation example.

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Section: System Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Overall recursive least squares and overall stochastic gradient algorithms and their convergence for feedback nonlinear controlled autoregressive systems

Wei

Xiao

et al. 2022

Intl J Robust & Nonlinear

Self Cite

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“…When the model of a dynamic system is established, one can design robust controllers for such a model to predict its dynamics in the future. ere exist many identification algorithms, for example, the least squares (LS) algorithm [4,5], the gradient descent (GD) algorithm [6,7], and the particle swarm optimization (PSO) algorithm [8,9]. When the considered model has a high order, the LS algorithm and the PSO algorithm are inefficient for their heavy computational efforts [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Exhaustive Search and Power‐Based Gradient Descent Algorithms for Time‐Delayed FIR Models

Chen

2022

Complexity

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In this study, two modified gradient descent (GD) algorithms are proposed for time-delayed models. To estimate the parameters and time-delay simultaneously, a redundant rule method is introduced, which turns the time-delayed model into an augmented model. Then, two GD algorithms can be used to identify the time-delayed model. Compared with the traditional GD algorithms, these two modified GD algorithms have the following advantages: (1) avoid a high-order matrix eigenvalue calculation, thus, are more efficient for large-scale systems; (2) have faster convergence rates, therefore, are more practical in engineering practices. The convergence properties and simulation examples are presented to illustrate the efficiency of the two algorithms.

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“…The concepts of the multi-innovation theory [63][64][65], auxiliary model idea [66,67], and hierarchical identification principle [68][69][70] can be integrated with the proposed methodology for better performance in system identification; moreover, the proposed scheme can be compared with other FO-PSO variants for solving complex optimization problems [71][72][73][74][75].…”

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confidence: 99%

Novel Fractional Swarming with Key Term Separation for Input Nonlinear Control Autoregressive Systems

et al. 2022

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In recent decades, fractional order calculus has become an important mathematical tool for effectively solving complex problems through better modeling with the introduction of fractional differential/integral operators; fractional order swarming heuristics are also introduced and applied for better performance in different optimization tasks. This study investigates the nonlinear system identification problem of the input nonlinear control autoregressive (IN-CAR) model through the novel implementation of fractional order particle swarm optimization (FO-PSO) heuristics; further, the key term separation technique (KTST) is introduced in the FO-PSO to solve the over-parameterization issue involved in the parameter estimation of the IN-CAR model. The proposed KTST-based FO-PSO, i.e., KTST-FOPSO accurately estimates the parameters of an unknown IN-CAR system with robust performance in cases of different noise scenarios. The performance of the KTST-FOPSO is investigated exhaustively for different fractional orders as well as in comparison with the standard counterpart. The results of statistical indices through Monte Carlo simulations endorse the reliability and stability of the KTST-FOPSO for IN-CAR identification.

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Hierarchical gradient- and least squares-based iterative algorithms for input nonlinear output-error systems using the key term separation

Cited by 109 publications

References 99 publications

Overall recursive least squares and overall stochastic gradient algorithms and their convergence for feedback nonlinear controlled autoregressive systems

Overall recursive least squares and overall stochastic gradient algorithms and their convergence for feedback nonlinear controlled autoregressive systems

Exhaustive Search and Power‐Based Gradient Descent Algorithms for Time‐Delayed FIR Models

Novel Fractional Swarming with Key Term Separation for Input Nonlinear Control Autoregressive Systems

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