Interval observer for LPV systems with unknown inputs

Meyer, Luc; Ichalal, Dalil; Vigneron, Vincent

doi:10.1049/iet-cta.2017.0788

Cited by 33 publications

(32 citation statements)

References 28 publications

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“…Choose G = R T Θ and H = R T Ω, we have GE + HC = I n . Second, we show that there exist matrices J i , L i satisfying (4) and (5). In fact, (4) and (5) can be rewritten as…”

Section: Preliminary Resultsmentioning

confidence: 86%

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Finite‐time observer design for singular systems subject to unknown inputs

Zhang

Chadli

Zhu

2019

IET Control Theory & Applications

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“…Choose G = R T Θ and H = R T Ω, we have GE + HC = I n . Second, we show that there exist matrices J i , L i satisfying (4) and (5). In fact, (4) and (5) can be rewritten as…”

Section: Preliminary Resultsmentioning

confidence: 86%

“…The studies on the unknown input observer (UIO) design have aroused considerable attention in the past decades [1][2][3][4][5][6]. Indeed, in practice, there are many situations in which partial inputs are inaccessible.…”

Section: Introductionmentioning

confidence: 99%

Finite‐time observer design for singular systems subject to unknown inputs

Zhang

Chadli

Zhu

2019

IET Control Theory & Applications

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“…[157]. For instance, a few recent works have merged UIOs with interval observers [158][159][160], in such a way that instead of a single trajectory for the estimation error, lower and upper bounds which are compatible with the uncertainty are computed. On the other hand, other works have considered the case in which the scheduling variables are measured inexactly, see for example, Refs.…”

Section: Unknown Input Observers-based Fault Isolationmentioning

confidence: 99%

A Review of Convex Approaches for Control, Observation and Safety of Linear Parameter Varying and Takagi-Sugeno Systems

2019

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This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).

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“…1 Interval observers are an attractive alternative for state estimation of uncertain systems, which, more precisely, are dynamical systems providing interval-valued trajectories of a given uncertain system. 2 Interval observers have been already considered for linear time invariant (LTI) systems; 1,3 linear time varying systems; 4 linear parameter varying systems; 5,6 systems subject to cyberattacks; 7 large-scale interconnected systems 8 ; descriptor systems; 9,10 nonlinear systems; 11,12 for stabilization; [13][14][15] and fault detection. [16][17][18] In interval observers, the bounds of uncertainty are needed as prior knowledge, for which however, only conservative values are known, resulting in the interval length between the upper and lower bounds of states being unnecessarily large.…”

Section: Introductionmentioning

confidence: 99%

“…Interval observers are an attractive alternative for state estimation of uncertain systems, which, more precisely, are dynamical systems providing interval‐valued trajectories of a given uncertain system 2 . Interval observers have been already considered for linear time invariant (LTI) systems; 1,3 linear time varying systems; 4 linear parameter varying systems; 5,6 systems subject to cyberattacks; 7 large‐scale interconnected systems 8 ; descriptor systems; 9,10 nonlinear systems; 11,12 for stabilization; 13‐15 and fault detection 16‐18 …”

Section: Introductionmentioning

confidence: 99%

A novel unknown input interval observer for systems not satisfying relative degree condition

Wang

Tan

Liu

et al. 2021

Intl J Robust & Nonlinear

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In this article, a novel unknown input interval observer (UIIO) is proposed for systems not satisfying the relative degree condition. In interval estimation, estimation errors are required not only positive but also convergent. For this purpose, some works combined unknown input observer with interval estimation, namely UIIO where by virtue of some transformations, some states are expressed as functions of outputs and other states which are decoupled from the unknown input. Nevertheless, complete decoupling can be guaranteed when the systems satisfy relative degree condition, which does not hold for some practical systems. Although some works have been done to relax the requirement on relative degree condition, they usually construct auxiliary outputs using high-order differentiators which necessitates that the signals are smooth enough as well as that their derivatives are bounded, limiting the application of existing approaches and also increasing the computational cost. Motivated by the discussions above, a novel UIIO scheme combining the interval observation technique with adaptive sliding mode is proposed, without the relative degree condition and free from differentiating signals, hence the design process is simplified and the computational cost is decreased. Finally, simulations are conducted to verify the effectiveness of the proposed scheme.

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Interval observer for LPV systems with unknown inputs

Cited by 33 publications

References 28 publications

Finite‐time observer design for singular systems subject to unknown inputs

Finite‐time observer design for singular systems subject to unknown inputs

A Review of Convex Approaches for Control, Observation and Safety of Linear Parameter Varying and Takagi-Sugeno Systems

A novel unknown input interval observer for systems not satisfying relative degree condition

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