Operator-based robust control design for nonlinear plants with perturbation

Bi, Shuhui; Deng, Mingcong

doi:10.1080/00207179.2011.582155

Cited by 36 publications

(19 citation statements)

References 16 publications

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“… Let X be a Banach space, if a Lipschitz operator J ∈ L i p ( X , X ) is satisfied with ‖ J ‖<1, then I − J is invertible, where I is the identity operator, and

‖ {(I - J)}^{- 1} ‖ \leq {(1 - ‖ J ‖)}^{- 1}

…”

Section: Mathematical Preliminaries and Problem Statementsmentioning

confidence: 99%

“… Let X and Z be Banach spaces, if G ∈ L i p ( X , Z ) is invertible and H is a Lipschitz operator from X to Z , such that

‖ H ‖ ‖ G^{- 1} ‖ < 1

Then, the operator H + G is invertible in L i p ( X , Z ) and

‖ {(H + G)}^{- 1} ‖ \leq ‖ G^{- 1} ‖ {(1 - ‖ H G^{- 1} ‖)}^{- 1}

…”

Section: Mathematical Preliminaries and Problem Statementsmentioning

confidence: 99%

“…Among these methods, an operator‐based left or right coprime factorization approach is proved to be a rather convenient framework for studying the nonlinear system. Many remarkable results and insight thoughts are obtained in different fields using left or right coprime factorization.…”

Section: Introductionmentioning

confidence: 99%

“…The right coprime factorization approach based on Lipschitz condition from operator view of point has been considered by many authors . In , robust right coprime factorization for nonlinear systems is considered firstly.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Control Method for Nonlinear Systems with Unknown Perturbations by Combining Left and Right Factorization

Tao

Deng

2017

Asian Journal of Control

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In this paper, nonlinear control design scheme for a class of nonlinear systems is proposed based on operator coprime factorization theory. In detail, two stable controllers are provided to design a Bezout identity by combining left factorization (not coprime) with right factorization. Based on the proposed design method, a realization approach to left coprime factorization for the nonlinear system is obtained, which provides an effective framework for constructing left coprime factorization. Meanwhile, internal‐output stability of the nonlinear system is guaranteed. After that, based on the obtained left coprime factorization, the cases of the nonlinear systems with perturbations are discussed for guaranteeing robust stability for the perturbed systems. For the perturbations, two different cases, known bounded perturbations and unknown bounded perturbations, are investigated from different viewpoints to analyze robust stability issue for the perturbed systems. Finally, a simulation example is given to confirm the effectiveness of the proposed design method.

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“… Let X be a Banach space, if a Lipschitz operator J ∈ L i p ( X , X ) is satisfied with ‖ J ‖<1, then I − J is invertible, where I is the identity operator, and

‖ {(I - J)}^{- 1} ‖ \leq {(1 - ‖ J ‖)}^{- 1}

…”

Section: Mathematical Preliminaries and Problem Statementsmentioning

confidence: 99%

“… Let X and Z be Banach spaces, if G ∈ L i p ( X , Z ) is invertible and H is a Lipschitz operator from X to Z , such that

‖ H ‖ ‖ G^{- 1} ‖ < 1

Then, the operator H + G is invertible in L i p ( X , Z ) and

‖ {(H + G)}^{- 1} ‖ \leq ‖ G^{- 1} ‖ {(1 - ‖ H G^{- 1} ‖)}^{- 1}

…”

Section: Mathematical Preliminaries and Problem Statementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear Control Method for Nonlinear Systems with Unknown Perturbations by Combining Left and Right Factorization

Tao

Deng

2017

Asian Journal of Control

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show abstract

“…It is well known that right coprime factorization has been a promising approach for analysis, design, stabilization and control of nonlinear system [5]. Especially, robust right coprime factorization has attracted much attention due to its convenient in researching input-output stability problems of nonlinear system [6,7,8,9]. On the whole, this approach has been proved effective in theoretical studies and practical applications on nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Operator based Robust Nonlinear Control Design to an Ionic Polymer Metal Composite with Uncertainties and Input Constraints

Wang¹,

Wei²,

Wang³

2014

Appl. Math. Inf. Sci.

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Abstract:In this paper, robust nonlinear control design to an ionic polymer metal composite (IPMC) with uncertainties and input constraints is studied. The IPMC is a novel smart polymer material, and many potential applications for low mass high displacement actuators in biomedical and robotic systems have been shown. In general, the IPMC has highly nonlinear property, and the control input is subject to some constraints to ensure safety and longer service life of IPMC. Moreover, there exist uncertainties caused by identifying some physical parameters and approximate calculation in dynamic model. As a result, considering measurement error of parameters and model error, a practical nonlinear model is obtained, and a nonlinear robust control design with uncertainties and input constraints using operator-based robust right coprime factorization is proposed. The effectiveness of the proposed control method based on obtained nonlinear model is confirmed by simulation and experimental results.

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References

2014

Operator‐Based Nonlinear Control Systems

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Operator-based robust control design for nonlinear plants with perturbation

Cited by 36 publications

References 16 publications

Nonlinear Control Method for Nonlinear Systems with Unknown Perturbations by Combining Left and Right Factorization

Nonlinear Control Method for Nonlinear Systems with Unknown Perturbations by Combining Left and Right Factorization

Operator based Robust Nonlinear Control Design to an Ionic Polymer Metal Composite with Uncertainties and Input Constraints

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