Multi-model decomposition of nonlinear dynamics using a fuzzy-CART approach

Gugaliya, Jinendra K.; Gudi, Ravindra D.; Lakshminarayanan, S.

doi:10.1016/j.jprocont.2004.07.004

Cited by 15 publications

(6 citation statements)

References 20 publications

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“…[32][33][34] The fermenter consists of two inputs and three outputs, namely feed substrate concentration (u 1 ), dilution rate (u 2 ), and biomass concentration (y 1 ), substrate concentration (y 2 ), production concentration (y 3 ). Following the same parameter setting and normal operating conditions given by Gugaliya et al, 33 a single input, single output (SISO) model between dilution rate (u 2 ) and biomass concentration (y 1 ) is identified. To ensure the local linearity of the identified model, a random binary signal with appropriate amplitude (from 0.1636 h À1 to 0.19 h À1 ) is designed for the input u 2 .…”

Section: Comparison Of Estimated Parameters Using Different Methods Wmentioning

confidence: 99%

Robust identification of piecewise/switching autoregressive exogenous process

Jin

Huang

2009

AIChE Journal

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A robust identification approach for a class of switching processes named PWARX (piecewise autoregressive exogenous) processes is developed in this article. It is proposed that the identification problem can be formulated and solved within the EM (expectation-maximization) algorithm framework. However, unlike the regular EM algorithm in which the objective function of the maximization step is built upon the assumption that the noise comes from a single distribution, contaminated Gaussian distribution is utilized in the process of constructing the objective function, which effectively makes the revised EM algorithm robust to the latent outliers. Issues associated with the EM algorithm in the PWARX system identification such as sensitivity to its starting point as well as inability to accurately classify ''un-decidable'' data points are examined and a solution strategy is proposed. Data sets with/without outliers are both considered and the performance is compared between the robust EM algorithm and regular EM algorithm in terms of their parameter estimation performance. Finally, a modified version of MRLP (multi-category robust linear programming) region partition method is proposed by assigning different weights to different data points. In this way, negative influence caused by outliers could be minimized in region partitioning of PWARX systems. Simulation as well as application on a pilot-scale switched process control system are used to verify the efficiency of the proposed identification algorithm.

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Section: Comparison Of Estimated Parameters Using Different Methods Wmentioning

confidence: 99%

Robust identification of piecewise/switching autoregressive exogenous process

Jin

Huang

2009

AIChE Journal

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“…A simulated CFR is employed in this section to verify the effectiveness of the proposed algorithm on nonlinear processes. The governing equation of the CFR system is provided as follows:

\begin{align} \overset{X}{true} & = prefix- D X + μ X, \\ \overset{S}{true} & = D false(S_{f} prefix- S false) prefix- \frac{1}{Y_{X false/ S}} μ X, \\ \overset{P}{true} & = prefix- D P + false(α μ + β false) X, \end{align}

where μ=μ m (1− P / P m ) S ( K m + S + S 2 / K i ) −1 is the specific growth rate. For the CFR system, the biomass concentration X , substrate concentration S , and product concentration P are state variables, while the dilution rate D and feed substrate concentration S f are manipulating variables.…”

Section: Simulation Examplementioning

confidence: 99%

“…A simulated CFR is employed in this section to verify the effectiveness of the proposed algorithm on nonlinear processes. The governing equation of the CFR system is provided as follows: [35][36][37] X = −DX + X,…”

Section: Process Descriptionmentioning

confidence: 99%

Online identification of time‐delay jump Markov autoregressive exogenous systems with recursive expectation‐maximization algorithm

Chen

Zhao

Liu

2020

Adaptive Control & Signal

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Summary This article considers the identification problem of the jump Markov autoregressive exogenous (JMARX) systems with unknown invariant time‐delay under the framework of recursive expectation‐maximization (REM) algorithm. In this article, a recursive Q‐function is formulated for the JMARX systems, based on which the recursive sufficient statistics are obtained. Then, the parameter vectors, variance, transition probability matrix, and time‐delay are recursively estimated. A numerical example and a simulated continuous fermentation reactor process are employed to illustrate the effectiveness of the proposed algorithm.

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“…The multimodel representation of this real system requires the decomposition of the system behavior into a set of local models with simple structures. The obtention of these partial models can be ensured by several methods . In this paper, an identification method based on the Levenberg‐Marquardt optimization algorithm is used.…”

Section: Experimental Validation Of the Proposed Multiobserver On A Tmentioning

confidence: 99%

A Sliding Mode Multiobserver Based on an Uncoupled Multimodel: An Application on a Transesterification Reaction

Montacer

Dehri

Atia

et al. 2018

Asian Journal of Control

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This paper concerns the design of robust sliding mode multiobserver for nonlinear systems. A discrete uncoupled multimodel structure is retained for the modeling of nonlinear systems. Unlike the classically used multimodel structures, the retained uncoupled multimodel is known by its flexibility of modeling, thus, the structures of the partial models are adapted to the complexity of the local models in each operating zone. Sufficient conditions are provided, in terms of linear matrix inequalities (LMIs), to ensure the asymptotic stability of the proposed sliding mode multiobserver. A convergence analysis is achieved to obtain the convergence radius. A numerical example and a real time application on a transesterification reactor are carried out to illustrate, once again, the performance of the proposed sliding mode multiobserver in terms of precision and rapidity of convergence.

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Multi-model decomposition of nonlinear dynamics using a fuzzy-CART approach

Cited by 15 publications

References 20 publications

Robust identification of piecewise/switching autoregressive exogenous process

Robust identification of piecewise/switching autoregressive exogenous process

Online identification of time‐delay jump Markov autoregressive exogenous systems with recursive expectation‐maximization algorithm

A Sliding Mode Multiobserver Based on an Uncoupled Multimodel: An Application on a Transesterification Reaction

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