A nonlinear Luenberger-like observer for nonlinear singular systems

Zheng, Gang; Boutat, Driss; Wang, Haoping

doi:10.1016/j.automatica.2017.08.018

Cited by 39 publications

(12 citation statements)

References 28 publications

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“…Therefore, the SPFM (47) is impulsive. The objective is to design a linear switching function as in (19) and SMC law (23) such that the closed-loop control system ( 24) is asymptotically stable. First, the parameter of switching function is given M = 2 3 and det(MB) = 5; therefore, the matrix M satisfies the design requirement.…”

Section: A Comparison Example With T-s Fuzzy Modelmentioning

confidence: 99%

“…The singular system is a natural representation of objective system. It can be used to describe further characteristics of the system and has been widely applied in large system theory, singular perturbed theory, circuit theory, and economic theory [19][20][21][22][23]. In 1999, Taniguchi et al combined the T-S fuzzy system with the singular system and promoted it to propose the T-S fuzzy singular system [24].…”

Section: Introductionmentioning

confidence: 99%

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The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach

Zhang

Jin

2021

Symmetry

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In this paper, the Singular-Polynomial-Fuzzy-Model (SPFM) approach problem and impulse elimination are investigated based on sliding mode control for a class of nonlinear singular system (NSS) with impulses. Considering two numerical examples, the SPFM of the nonlinear singular system is calculated based on the compound function type and simple function type. According to the solvability and the steps of two numerical examples, the method of solving the SPFM form of the nonlinear singular system with (and without) impulse are extended to the more general case. By using the Heine–Borel finite covering theorem, it is proven that a class of nonlinear singular systems with bounded impulse-free item (BIFI) properties and separable impulse item (SII) properties can be approximated by SPFM with arbitrary accuracy. The linear switching function and sliding mode control law are designed to be applied to the impulse elimination of SPFM. Compared with some published works, a human posture inverted pendulum model example and Example 3.2 demonstrate that the approximation error is small enough and that both algorithms are effective. Example 3.3 is to illustrate that sliding mode control can effectively eliminate impulses of SPFM.

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Section: A Comparison Example With T-s Fuzzy Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach

Zhang

Jin

2021

Symmetry

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“…where Π 12 and Π 22 are defined as (28) and (29), respectively. In this case, the gain matrices of the observer (36) are computed as…”

Section: B Extension To Lipschits Nonlinear Singular Systemsmentioning

confidence: 99%

Proportional-Difference Observer Design for Singular Systems in an LMI Framework

Ren

2020

IEEE Access

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This paper deals with the problem of proportional-difference observer design for singular systems in the discrete-time domain. Several necessary and sufficient conditions for the existence and convergence of the proposed observer are given and proved. Without using any additional transformations, a necessary and sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequalities. The explicit expression of desired observer is also given. Furthermore, an extension to a class of nonlinear singular systems with Lipschitz constraints is investigated. Finally, a practical example and a numerical one are simulated to illustrate the effectiveness of the proposed approaches.

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“…The effect ofθ andφ in the dynamics of the eigenvalues is compensated, using the camera's angular velocity. It is computed by setting (24) and (25) to zero and solving for ω c yielding…”

Section: Observer Design and Active Estimationmentioning

confidence: 99%

Active Estimation of 3D Lines in Spherical Coordinates

Mateus

Tahri

Miraldo

2019

2019 American Control Conference (ACC)

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Straight lines are common features in human made environments, which makes them a frequently explored feature for control applications. Many control schemes, like Visual Servoing, require the 3D parameters of the features to be estimated. In order to obtain the 3D structure of lines, a nonlinear observer is proposed. However, to guarantee convergence, the dynamical system must be coupled with an algebraic equation. This is achieved by using spherical coordinates to represent the line's moment vector, and a change of basis, which allows to introduce the algebraic constraint directly on the system's dynamics. Finally, a control law that attempts to optimize the convergence behavior of the observer is presented. The approach is validated in simulation, and with a real robotic platform with a camera onboard.

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A nonlinear Luenberger-like observer for nonlinear singular systems

Cited by 39 publications

References 28 publications

The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach

The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach

Proportional-Difference Observer Design for Singular Systems in an LMI Framework

Active Estimation of 3D Lines in Spherical Coordinates

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