Robust identification of systems using block-pulse functions

Dai, H.; Sinha, Ν.Κ.

doi:10.1049/ip-d.1992.0042

Cited by 9 publications

(4 citation statements)

References 2 publications

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“…Then, the state estimation errorx k given by (8) is exponentially bounded in mean square and bounded with probability one.…”

Section: Lemmamentioning

confidence: 99%

“…Specifically, much attractive attention has been paid to bilinear systems as they are simple nonlinear systems and represent the intermediary structure between linear models and nonlinear models. 8 Hizir et al identified the bilinear systems through equivalent linear models. 7 Dai and Sinha utilized the block functions for parameter estimation of the bilinear system.…”

Section: Introductionmentioning

confidence: 99%

“…7 Dai and Sinha utilized the block functions for parameter estimation of the bilinear system. 8 Hizir et al identified the bilinear systems through equivalent linear models. 9 Nowadays, the Carleman linearization is an approach to reach the approximation, and the bilinear model is proven to be an effective approximator for some nonlinear systems, which can solve the nonlinear system state filtering problems in signal processing and control.…”

Section: Introductionmentioning

confidence: 99%

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State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

Xiao

Ding

Yang

2019

Adaptive Control & Signal

223

117

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This paper considers the state estimation problem of bilinear systems in the presence of disturbances. The standard Kalman filter is recognized as the best state estimator for linear systems, but it is not applicable for bilinear systems.It is well known that the extended Kalman filter (EKF) is proposed based on the Taylor expansion to linearize the nonlinear model. In this paper, we show that the EKF method is not suitable for bilinear systems because the linearization method for bilinear systems cannot describe the behavior of the considered system. Therefore, this paper proposes a state filtering method for the single-input-single-output bilinear systems by minimizing the covariance matrix of the state estimation errors. Moreover, the state estimation algorithm is extended to multiple-input-multiple-output bilinear systems. The performance analysis indicates that the state estimates can track the true states. Finally, the numerical examples illustrate the specific performance of the proposed method.

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“…Then, the state estimation errorx k given by (8) is exponentially bounded in mean square and bounded with probability one.…”

Section: Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

Xiao

Ding

Yang

2019

Adaptive Control & Signal

223

117

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“…Parameter estimation of bilinear systems is supposed to consider the existence of the bilinear term, which makes the identification more difficult than that of the linear systems. Bilinear modelling approaches such as Walsh functions (Karanam, Frick, & Mohler, 1978), block functions (Dai & Sinha, 1992), Hartley modulating functions (Daniel-Berhe & Unbehauen, 1998) and Volterra series (Inagaki & Mochizuki, 1984) have been widely studied. In the literature, Vicario, Phan, and Betti (2014) proposed an intersection subspace algorithm to identify a bilinear system by using the interaction matrices to establish the relationship between the bilinear states with input-output data.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical parameter and state estimation for bilinear systems

Zhang

Ding

2020

International Journal of Systems Science

153

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The identification of state-space models of bilinear systems is studied in this paper. The parameters to be identified of the considered system are coupled with the unknown states, which makes the identification problem more difficult than that of the linear state-space model. For the coupled variables, this paper introduces the interaction estimation theory to study an on-line algorithm for joint state-parameter estimation. To be more specific, a state observer in the bilinear form is established by minimising the state estimation error covariance matrix in the same way of a Kalman filter on the condition that the parameters are known. Then, a bilinear state observer based recursive least squares algorithm is developed using the least squares method. Moreover, for the purpose of improving the computational efficiency, a bilinear state observer based two-stage recursive least squares algorithm and a bilinear state observer based multi-stage recursive least squares algorithm are proposed by decomposing the system into several subsystems based on the hierarchical identification. Finally, a numerical simulation is employed to show the specific performance of the proposed approaches.

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Stabilization of spectral methods for the analysis of singular systems using piecewise constant basis functions

Caiti

Cannata

1995

Circuits Systems and Signal Process

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Robust identification of systems using block-pulse functions

Cited by 9 publications

References 2 publications

State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

Hierarchical parameter and state estimation for bilinear systems

Stabilization of spectral methods for the analysis of singular systems using piecewise constant basis functions

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