Unknown Input and State Estimation for Unobservable Systems

Bejarano, Francisco Javier; Poznyak, Alexander S.

doi:10.1137/070700322

Cited by 76 publications

(64 citation statements)

References 16 publications

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“…Under the condition that the norm of the uncertain term ε(x, t) fulfills the restriction (29), the proposed estimation procedure given by (26), (28) provides the exact reconstruction of the binary vector δ in the time intervals t ∈ [t i−1 + t * , t i ), according to (30). would correspond, in the linear context, to locating the eigenvalues of the error dynamics far away from the origin.…”

Section: Lemmamentioning

confidence: 99%

“…Recently several methodologies have been proposed in the literature for the finite time reconstruction of unknown inputs based on higher-order sliding mode theory, via the so-called hierarchical HOSM observation approach [27,28]. In this paper a finite time observer based on the sub-optimal sliding mode algorithm will be suggested, which provides the exact unknown input reconstruction and a guaranteed convergence time in spite of model uncertainties.…”

Section: Introductionmentioning

confidence: 99%

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Robust reconstruction of the discrete state for a class of nonlinear uncertain switched systems

Orani

Pisano

Franceschelli

et al. 2011

Nonlinear Analysis: Hybrid Systems

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This paper presents an approach to the robust state reconstruction for a class of\ud nonlinear switched systems affected by model uncertainties. Under the assumption that\ud the continuous state is available for measurement, an approach is presented based on\ud concepts and methodologies derived from the sliding mode control theory. With noisefree\ud state measurements, the time needed for reconstructing the discrete state after a\ud transition can be made arbitrarily small by sufficiently increasing a certain observer tuning\ud parameter. Simulations and experiments, carried out on a three-tank laboratory setup, are presented and commented

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Section: Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust reconstruction of the discrete state for a class of nonlinear uncertain switched systems

Orani

Pisano

Franceschelli

et al. 2011

Nonlinear Analysis: Hybrid Systems

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“…39 Therefore, the method of finite-time estimation in section ''Finite time observation for strongly observable systems'' can be utilized to reconstruct "…”

Section: Construct Nonsingular Matrixmentioning

confidence: 99%

Fast fault estimation for linear systems with unmatched faults

Zhao

Huang

2015

Proceedings of the Institution of Mechanical Engineers, Part G:

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This paper proposes a fast fault estimation (FE) method for a class of linear time-invariant systems, which relaxes the strict observer matching condition. Firstly, the integration unknown input observer is designed for the more widely left invertible systems. Secondly, for strongly observable systems, by digesting the idea of a finite-time observer, the finitetime integration unknown input observer is designed, and the faults are estimated exactly in pre-designed arbitrary finite time. Furthermore, for strongly detectable systems, after the system decomposed into strongly observable part and nonstrongly observable part, faults are able to be reconstructed very rapidly due to the finite-time observation of the strongly observable subsystem. The simulation results illustrate the effectiveness and the advantage of the proposed fast fault estimation schemes.

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“…The first drawback has to do with the assumption that the system is strongly detectable but not strongly observable; therefore, a transformation must first be done in order to decompose the system into the strongly observable part and the detectable part (see, e.g. [16]). The second drawback has to do with the fact that, during the implementation of the differentiator, some errors appear due to the computation sample time and noises in the sensors.…”

Section: B Output Extension Via Hosm Differentiatormentioning

confidence: 99%

“…Some observers have been designed assuming that the Hautus condition is satisfied ( [10], [11], [2]). In some other works, a differentiation process was suggested, mainly based on first and second order sliding mode techniques ( [12], [3], [13], [14], [15], [16]). A method for the construction of a new output to fulfill the Hautus condition is suggested in [17].…”

Section: Introductionmentioning

confidence: 99%

Unbounded unknown inputs estimation based on high-order sliding mode differentiator

Bejarano

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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An observer is designed for strongly detectable systems with unbounded unknown inputs. The design scheme is based on three steps. First, the system is extended taking the unknown inputs (and possibly some of their derivatives) as new states. Then, using a high-order sliding mode differentiator (HOSMD), a new output of the system is generated in order to fulfill the Hautus condition. Finally, the system is decomposed into two subsystem, the first one being unaffected directly by the unknown inputs, and the second subsystem being obtained directly from the system output. Thus, a Luenberger observer is designed for the first subsystem. This procedure allows one to estimate the state and the unknown inputs using the least number of differentiations possible. Some simulations are given to show the effectiveness of the proposed observer.

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Unknown Input and State Estimation for Unobservable Systems

Cited by 76 publications

References 16 publications

Robust reconstruction of the discrete state for a class of nonlinear uncertain switched systems

Robust reconstruction of the discrete state for a class of nonlinear uncertain switched systems

Fast fault estimation for linear systems with unmatched faults

Unbounded unknown inputs estimation based on high-order sliding mode differentiator

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