On LMI conditions to design observers for Lipschitz nonlinear systems

Zemouche, Ali; Boutayeb, Mohamed

doi:10.1016/j.automatica.2012.11.029

Cited by 305 publications

(250 citation statements)

References 19 publications

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Section: Lemmamentioning

confidence: 99%

“…For more details about the functions Φ ij in Equation 27, see lemma 6 in the work of Zemouche and Boutayeb. 27 It should be noted that all the existing approaches developed for fault estimation assume that the Lipschitz constant is the same for each component of the nonlinear function. As stated in the work of Zemouche and Boutayeb, 27 the use of the classical Lipschitz condition generally cannot provide a feasible solution for systems with large Lipschitz constants.…”

Section: Lemmamentioning

confidence: 99%

“…27 It should be noted that all the existing approaches developed for fault estimation assume that the Lipschitz constant is the same for each component of the nonlinear function. As stated in the work of Zemouche and Boutayeb, 27 the use of the classical Lipschitz condition generally cannot provide a feasible solution for systems with large Lipschitz constants. Lemma 1 takes into account the detailed structure of the nonlinear function and obtains lower and upper bounds for each of its component, which can guarantee nonrestrictive synthesis conditions.…”

Section: Lemmamentioning

confidence: 99%

“…To solve this problem, a linear parameter-varying (LPV) approach has been proposed in the work of Zemouche and Boutayeb 27 that introduces a less conservative Lipschitz property and thus provides less restrictive synthesis conditions. Furthermore, it is worth noticing that all the aforementioned FE approaches were considered in the full frequency domain, which cannot always meet the requirements of practical systems since the frequency ranges of faults and disturbances may have different frequency characteristics.…”

Section: Introductionmentioning

confidence: 99%

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Simultaneous actuator and sensor fault estimation for discrete‐time Lipschitz nonlinear systems in finite‐frequency domain

Yang

2017

Optim Control Appl Methods

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SummaryThis paper addresses the problem of actuator and sensor fault reconstruction simultaneously with finite-frequency specifications for discrete-time Lipschitz nonlinear systems. First, an augmented system description is given by extending the sensor fault as an auxiliary state vector. Then, a multiobjective unknown input proportional-integral observer is designed, and the nonlinear error dynamics are transformed into a linear parameter-varying system based on the use of a reformulated Lipschitz property. Sufficient conditions for the design of a fault estimator with 2 finite-frequency H ∞ performances are derived in terms of linear matrix inequalities where a slack variable is introduced to reduce the conservativeness of the design. The proposed method can provide less restrictive linear matrix inequality conditions and get a better fault estimation performance than the existing one in the full frequency domain. Simulation results are given to show the effectiveness of the proposed techniques.

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Section: Lemmamentioning

confidence: 99%

Section: Lemmamentioning

confidence: 99%

Section: Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simultaneous actuator and sensor fault estimation for discrete‐time Lipschitz nonlinear systems in finite‐frequency domain

Yang

2017

Optim Control Appl Methods

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“…Lipschitz observer is a common non-linear system state observer and still has a good observation performance for strongly non-linear systems with noise disturbances. Specific design process of Lipschitz observer is characterized as follows (Rajamani 1998;Zemouche and Boutayeb 2013;Pourgholi and Majd 2011).…”

Section: Fast Loop Controller Designmentioning

confidence: 99%

The Control of Asymmetric Rolling Missiles Based on Improved Trajectory Linearization Control Method

Sun¹,

Yu²,

Zhang³

2016

J.Aerosp. Technol. Manag.

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According to motion characteristic of an asymmetric rolling missile with damage fin, a three-channel controlled model is established. The controller which is used to realize non-linear tracking and decoupling control of the roll and angle motion is introduced based on an improved trajector y linearization control method. The improved method is composed of the classic trajectory linearization control method and a compensation control law. The classic trajectory linearization control method is implemented in the time-scale separation principle. The Lipschitz non-linear state observer systematically obtained by solving the linear matrix inequality approach is provided to estimate state variables and unknown parameters, and then the compensation control law utilizing the estimated unknown parameters improves the TLC method. Simulation experiments show that the adaptive decoupling control ensure tracking performance, and the robustness and accuracy of missile attitude control are ensured under the condition of the system parameters uncertainty, random observation noise and external disturbance caused by damage fin.

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Robust H_∞ sliding mode observer‐based fault‐tolerant control for One‐sided Lipschitz nonlinear systems

Rastegari

Arefi

Asemani

2019

Asian Journal of Control

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This paper presents fault tolerant controllers for a class of one-sided Lipschitz nonlinear systems with external disturbances. A sliding mode observer (SMO) is integrated with the H ∞ filtering approach as the fault detection and isolation module. The problem is investigated in the presence of faults and disturbances simultaneously. The H ∞ -SMO is capable of approximating faults accurately, while reducing the effect of disturbances in the estimation of the state vector and occurred faults. Accordingly, using only a single SMO, the estimation error of the state vector and faults can be made simultaneously arbitrarily small. In addition, to deal with the weighted bilinear form appearing in the one-sided Lipschitz condition, the quadratically inner bounded condition presented in the literature is employed in this paper as a useful solution. The proposed method guarantees the stability of the overall closed-loop system, and after a short transient time, the estimation errors for state vector and fault signal converge to a small neighborhood of the origin. The effectiveness of the presented algorithm is confirmed in two examples including a single arm robot with a flexible joint and a numerical simulation.

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On LMI conditions to design observers for Lipschitz nonlinear systems

Cited by 305 publications

References 19 publications

Simultaneous actuator and sensor fault estimation for discrete‐time Lipschitz nonlinear systems in finite‐frequency domain

Simultaneous actuator and sensor fault estimation for discrete‐time Lipschitz nonlinear systems in finite‐frequency domain

The Control of Asymmetric Rolling Missiles Based on Improved Trajectory Linearization Control Method

Robust H_∞ sliding mode observer‐based fault‐tolerant control for One‐sided Lipschitz nonlinear systems

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On LMI conditions to design observers for Lipschitz nonlinear systems

Cited by 305 publications

References 19 publications

Simultaneous actuator and sensor fault estimation for discrete‐time Lipschitz nonlinear systems in finite‐frequency domain

Simultaneous actuator and sensor fault estimation for discrete‐time Lipschitz nonlinear systems in finite‐frequency domain

The Control of Asymmetric Rolling Missiles Based on Improved Trajectory Linearization Control Method

Robust H∞ sliding mode observer‐based fault‐tolerant control for One‐sided Lipschitz nonlinear systems

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Robust H_∞ sliding mode observer‐based fault‐tolerant control for One‐sided Lipschitz nonlinear systems