Adaptive impulsive observers for nonlinear systems: Revisited

Chen, Wu‐Hua; Yang, Wu; Zheng, Wei Xing

doi:10.1016/j.automatica.2015.08.018

Cited by 50 publications

(31 citation statements)

References 29 publications

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“…PD − C T F T ≤ 0 (18) are feasible for a matrix 0 < P T = P ∈ R n×n , matrices F ∈ R l× , L ∈ R n× , and constants , r, > 0, then system (14), with k = ||w|| ∞ , is ISS with respect to inputs̃and w. Moreover, its trajectories satisfy the following bounds:…”

Section: Lemmamentioning

confidence: 99%

“…3. The condition (18) introduces structural restrictions over the triple (A, D, C); specifically, it must not have invariant zeros, and the relative degree of output y with respect to input w must be equal to one. In order to avoid these restrictions, some approaches were proposed in the works of Efimov and Fradkov 28 and Edwards et al 29…”

Section: Convergence Of the Adaptive Observermentioning

confidence: 99%

“…Adaptive impulsive observers were proposed by Chen et al 18 and Efimov and Fradkov 19 for a class of nonlinear systems. Particularly, in the work of Chen et al, 18 the proposed observer was modeled by an impulsive differential equation, the asymptotic convergence was analyzed based on a time-varying Lyapunov function approach, and some sufficient conditions were formulated in terms of linear matrix inequalities (LMIs). On the other hand, in the work of Efimov and Fradkov, 19 a new impulsive adaptive observer showed that an impulsive feedback can improve the convergence rate or relax the requirement on persistency of excitation.…”

Section: Introductionmentioning

confidence: 99%

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An adaptive sliding‐mode observer for a class of uncertain nonlinear systems

Ríos

Efimov

Perruquetti

2018

Adaptive Control & Signal

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In this paper, the problem of simultaneous state and parameter estimation is studied for a class of uncertain nonlinear systems. A nonlinear adaptive sliding-mode observer is proposed based on a nonlinear parameter estimation algorithm. It is shown that such a nonlinear algorithm provides a rate of convergence faster than exponential, ie, faster than the classic linear algorithm. Then, the proposed parameter estimation algorithm is included in the structure of a sliding-mode state observer, providing an ultimate bound for the full estimation error and attenuating the effects of the external disturbances. Moreover, the synthesis of the observer is given in terms of linear matrix inequalities. The corresponding proofs of convergence are developed based on the Lyapunov function approach and input-to-state stability theory. Some simulation results illustrate the efficiency of the proposed adaptive sliding-mode observer.

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Section: Lemmamentioning

confidence: 99%

Section: Convergence Of the Adaptive Observermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An adaptive sliding‐mode observer for a class of uncertain nonlinear systems

Ríos

Efimov

Perruquetti

2018

Adaptive Control & Signal

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“…For each subsystem i ∈ M , the parameter adaptive law to be designed is defined as follows:

\overset{\overset{θ}{true}}{true} (t) = φ (t) normal Γ {normal Φ}_{1 i}^{T} (\overset{x}{true} (t), u (t)) H_{i} (t) ([], y (t) - C_{i} \overset{x}{true} (t)),

where Γ∈ R r × r is an arbitrary positive definite matrix.…”

Section: Problem Formulationmentioning

confidence: 99%

Adaptive Impulsive Observers for a Class of Switched Nonlinear Systems with Unknown Parameter

Dimirovski

2017

Asian Journal of Control

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This work investigates and solves the design of adaptive impulsive observers for a class of uncertain switched nonlinear systems with unknown parameter. Sufficient conditions are derived for designing such observers for each subsystem to reconstruct asymptotically and update system states in real time. The state observer is represented in terms of impulsive differential equations. The parameter estimation law is modelled by an impulse‐free, time‐varying differential equation associated with the impulse time sequence in order to determine when the observer estimated state is updated. The asymptotic convergence to zero of the observation errors is established by applying the method of multiple time‐varying Lyapunov functions. Sufficient conditions are derived that guarantee the convergence of parameter estimation. An example of switched Lorenz system along with numeric and simulation results is presented to demonstrate the effectiveness of the proposed method.

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“…Impulsive observer dynamics are described by impulsive differential equations, with the observer state updated only at discrete instants. Among the other benefits (see [23] for further advantages), this allows reducing the use of the bandwidth usage, and therefore, impulsive observers are very appealing in the control of networked systems.In this work, impulsive observers are used to estimate the state of a class of nonlinear Lipschitz systems, where the sensor data are communicated via the wireless channel, using the aforementioned periodic event-triggered mechanism. Hence, not only the output is not available continuously but one also loses the advantage of the classic approach with periodic sampling, allowing the closed-loop system to be analyzed on the basis of sampled-data formalism [24].…”

mentioning

confidence: 99%

Periodic event‐triggered observation and control for nonlinear Lipschitz systems using impulsive observers

Etienne

Gennaro

Barbot

2017

Intl J Robust & Nonlinear

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International audienceIn this paper, we investigate the observation and stabilization problems for a class of nonlinear Lipschitz systems, subject to network constraints, and partial state knowledge. In order to address these problems, an impulsive observer is designed, making use of the event-triggered technique in order to diminish the network communications. Sufficient conditions are given to ensure a milder version of the separation principle for these systems, controlled via an event-triggered controller. The proposed observer ensures practical state estimation, while the corresponding dynamic controller ensures practical stabilization. The sampling and the data transmission are carried out asynchronously. The dynamic controller is tested in simulation on a flexible joint

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Adaptive impulsive observers for nonlinear systems: Revisited

Cited by 50 publications

References 29 publications

An adaptive sliding‐mode observer for a class of uncertain nonlinear systems

An adaptive sliding‐mode observer for a class of uncertain nonlinear systems

Adaptive Impulsive Observers for a Class of Switched Nonlinear Systems with Unknown Parameter

Periodic event‐triggered observation and control for nonlinear Lipschitz systems using impulsive observers

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