Unknown input observer for linear time-delay systems

Zheng, Gang; Bejarano, Francisco Javier; Perruquetti, Wilfrid; Richard, Jean‐Pierre

doi:10.1016/j.automatica.2015.07.029

Cited by 53 publications

(27 citation statements)

References 27 publications

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“…Comparing with the asymptotic observer proposed in Zheng et al (2015), after the transition, the convergent speed of the proposed finite-time observer is nonlinear (much faster than linear one depicted in Figure 1), and finally stays around very small estimation error (around 10 −20 due to numerical algorithm used to simulate system). Finally, Figure 3 plots the estimation error of the unknown input w(t), which clearly shows that the estimation is finite-time.…”

Section: Academic Examplementioning

confidence: 99%

Section: Academic Examplementioning

confidence: 99%

“…In order to show the effectiveness of the proposed finite-time observer, we compared our results with respect to that of Zheng et al (2015) with the same gains. Firstly we plot (in Figure 1) the estimation errors by using the observer proposed in Zheng et al (2015). From Figure 1, we can see that after the period of transition (the jumps are due to the zero cross of estimation error when calculating the log value), the convergent speed is linear, which corresponds exactly to the asymptotic estimation case.…”

Section: Academic Examplementioning

confidence: 99%

“…This method was extended to treat unknown input case by Zheng et al (2015). This paper will show how to adapt the results of Hou et al (2002) and Zheng et al (2015) to design a finite-time observe for (2) by using homogeneous technique.…”

Section: Problem Statementmentioning

confidence: 99%

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Finite-time estimation for linear time-delay systems via homogeneous method

Zheng

Wang

2017

International Journal of Control

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This paper presents a finite-time observer for linear time-delay systems with commensurate delay. Unlike the existing observers in the literature which converge asymptotically, the proposed observer provides a finite-time estimation. This is realized by using the well-known homogeneous technique, and the results are also extended to investigate the estimation problem for linear time-delay systems with unknown inputs. Simulation results are presented in order to illustrate the feasibility of the proposed method.

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Section: Academic Examplementioning

confidence: 99%

Section: Academic Examplementioning

confidence: 99%

Section: Academic Examplementioning

confidence: 99%

Section: Problem Statementmentioning

confidence: 99%

See 2 more Smart Citations

Finite-time estimation for linear time-delay systems via homogeneous method

Zheng

Wang

2017

International Journal of Control

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“…In fact, left invertibility problem has been studied since at least forty five years ago in linear control theory [33], [34] and thirty five year ago in nonlinear control theory [15], [35]. Most of those works are in the context of nonlinear systems without time delays, or linear systems with commensurate delays [2], [41].…”

Section: Introductionmentioning

confidence: 99%

Finite-time and asymptotic left inversion of nonlinear time-delay systems

2018

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In this paper we investigate the left invertibility problem for a class of nonlinear time-delay systems. In both cases of time delay systems with and without internal dynamics the invertibility conditions are given. A new approach based on the use of higher order sliding mode observer is developed for finite-time left invertibility and for asymptotic left inversion. Causal and non-causal estimation of the unknown inputs are respectively discussed. The results are illustrated by numerical examples in order to show the efficiency of the method and its limits.Key words: Left inversion, nonlinear system, nonlinear time-delay system, asymptotic left inversion, internal dynamics. IntroductionTime delay systems represent one of the most studied class of systems in control theory. Since the 60', many different problems are studied such as stability and stabilization of time delay systems, observation and observer design, parameter identification, etc. In the present work we are interested in the left invertibility problem of time delay systems with internal dynamics. The problem of unknown inputs recovering from the outputs is crucial. Such a problem has attracted the interest of the control community since it has direct applications in many domains, such as data secure transmission where the unknown input is the message, and fault detection and isolation where the fault is the unknown input. In fact, left invertibility problem has been studied since at least forty five years ago in linear control theory [33] In the literature, an important tool based on non-commutative ring, proposed in [36], is used to analyze nonlinear time delay systems in algebraic framework. Using this framework, many notions are extended to the case of nonlinear time * Corresponding author.Email address: zohra.kader@inria.fr (Zohra Kader). delay systems and many results have already been obtained and published [40], [37]. In the context of constant time delay, the notions of Lie derivatives and relative degree are defined, and the differences between causal and non-causal invertibility are clarified in [38]. The canonical form of invertibility is also given in [39], and in [42] a method for estimating the unknown inputs is proposed. However, the algorithm for left invertibility proposed in [39] was only for system without internal dynamics (see also [4] and [13] and their references). For system with or without time-delay, the main difficulty when the internal dynamics appears is to estimate the state of such dynamics. One interesting solution in order to overcome such a difficulty is to allow the derivative of the unknown inputs [31] with a geometrical approach and with an algebraic one. If, however, the input derivatives are not possible, then it is necessary to compute and analyze the internal dynamics.For nonlinear systems without delay, if the vector fields associated to the inputs verify involutivity property, then the internal dynamics does not depend on the unknown input. However, this rule is not valid for nonlinear systems with...

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Fault diagnosis by interval‐based adaptive thresholds and peak‐to‐peak observers

Wang

Meslem

et al. 2022

Adaptive Control & Signal

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This article investigates actuator fault diagnosis for continuous-time systems with unknown but bounded uncertainties. A novel interval-based adaptive threshold computation approach is proposed for residual evaluation. Meanwhile, peak-to-peak performance is applied to generate robust residuals against system uncertainties. By integrating the designed peak-to-peak residual generator with adaptive thresholds, we can achieve promising fault detection results.Furthermore, based on the general observer scheme, the proposed residual generator and adaptive thresholds can be equally used for fault isolation. Simulation results are given to illustrate the effectiveness and superiority of the proposed fault detection and isolation method.

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Unknown input observer for linear time-delay systems

Cited by 53 publications

References 27 publications

Finite-time estimation for linear time-delay systems via homogeneous method

Finite-time estimation for linear time-delay systems via homogeneous method

Finite-time and asymptotic left inversion of nonlinear time-delay systems

Fault diagnosis by interval‐based adaptive thresholds and peak‐to‐peak observers

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