Observer for Lipschitz nonlinear systems: Mean Value Theorem and sector nonlinearity transformation

Ichalal, Dalil; Marx, Benoît; Mammar, Saïd; Maquin, Didier; Ragot, José

doi:10.1109/isic.2012.6398269

Cited by 10 publications

(4 citation statements)

References 23 publications

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“…The major head loss of a pipe from node i to j is due to friction and is determined by (5) from Tab. II, where R is the resistance coefficient and µ is the constant flow exponent in the Hazen-Williams formula.…”

Section: A Models Of Components 1) Tanks and Reservoirsmentioning

confidence: 99%

Computing Lipschitz Constants for Hydraulic Models of Water Distribution Networks

Shadfan¹,

Wang²,

Nugroho³

et al. 2020

Preprint

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Drinking water distribution networks (WDN) are large-scale, dynamic systems spanning large geographic areas. Water networks include various components such as junctions, reservoirs, tanks, pipes, pumps, and valves. Hydraulic models for these components depicting mass and energy balance form nonlinear algebraic differential equations (NDAE). While control theoretic studies have been thoroughly explored for other complex infrastructure such as power and transportation systems, little is understood or even investigated for feedback control and state estimation problems for the NDAE models of WDN. The objective of this paper is to showcase a complete NDAE model of WDN followed by computing Lipschitz constants of the vector-valued nonlinearity in that model. The computation of Lipschitz constants of hydraulic models is crucial as it paves the way to apply a plethora of control-theoretic studies for water system applications. In particular, the computation of Lipschitz constant is explored through closed-form, analytical expressions as well as via numerical methods. Case studies reveal how such computations fare against each other for various water networks.

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Section: A Models Of Components 1) Tanks and Reservoirsmentioning

confidence: 99%

Computing Lipschitz Constants for Hydraulic Models of Water Distribution Networks

Shadfan¹,

Wang²,

Nugroho³

et al. 2020

Preprint

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“…The MVT is then applied to the Lipchitz terms in (10), such that [12,13] where ∈ [a, b] such that: represent the premise variables. Then, one can replace the derivatives of (11) by: Subsequently using (12), Eq.…”

Section: Non-linear Observer Design With Mvtmentioning

confidence: 99%

Sensorless Non-linear Control Applied to a PMSM Machine Based on New Extended MVT Observer

Hamidani¹,

Allag²,

Zeghib³

2019

J. Electr. Eng. Technol.

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The focus of this paper is on the notion of an extended observer based on Input-output feedback linearization control. The mean value theorem (MVT) and sector non-linearity approaches were implemented for a class of the Lipchitz model of Permanent Magnet Synchronous Machine (PMSM). Based on these mathematical approaches, the proposed design allows the expression of nonlinear error dynamics for the extended observer become a convex combination of known matrices that have time varying coefficients. This is similar to a linear parameter varying (LPV) systems after the non-linear system of the PMSM is represented in the Lipchitz form. Through the Lyapunov theory, one can obtain and express the stability conditions in a term of linear matrix inequalities (LMI). The extended observer gain is separately determined based on the separation principles by the exploitation of YALMIP software. Furthermore, this gain have complete independence from the PMSM states. As a proof of the efficacy of the proposed approach, one applies an illustrative simulation to the sensorless Field Oriented Control (FOC) of the PMSM drive by utilising the MATLAB/SIMULINK environment.

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“…In the work of Zemouche et al, the observers' design for a class of nonlinear dynamic systems without unknown inputs was studied. In the work of Ichalal et al, the dynamics of state estimation errors was written in Takagi‐Sugeno system (this system type is consider by several authors) form using the mean value theorem and the sector nonlinearity transformation. The design developed in the work of Zemouche et al was used for the observer design of an induction motor system .…”

Section: Introductionmentioning

confidence: 99%

“…In the work of Ichalal et al, the dynamics of state estimation errors was written in Takagi‐Sugeno system (this system type is consider by several authors) form using the mean value theorem and the sector nonlinearity transformation. The design developed in the work of Zemouche et al was used for the observer design of an induction motor system . In the work of Sharma et al, an extension for unknown input observer for nonlinear discrete and continuous systems using the mean value theorem was discussed.…”

Section: Introductionmentioning

confidence: 99%

Observer for nonlinear systems with unknown input using mean value theorem and genetic algorithm

Messaoud

Hajji

2018

Optim Control Appl Methods

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In this note, we consider a new unknown inputs observer design for nonlinear systems. The main idea consists in determining the estimation error and theorem mean value parameters to introduce them into the proposed observer structure. This process is designed on the basis of mean value theorem and genetic algorithm. This observer does not use LMI technique for stability study.The stability study relies on the use of quadratic Lyapunov function. Two numerical examples are provided to show the performance of the proposed approach.KEYWORDS genetic algorithm, mean value theorem, nonlinear system, state estimation, unknown input observer 1904

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Observer for Lipschitz nonlinear systems: Mean Value Theorem and sector nonlinearity transformation

Cited by 10 publications

References 23 publications

Computing Lipschitz Constants for Hydraulic Models of Water Distribution Networks

Computing Lipschitz Constants for Hydraulic Models of Water Distribution Networks

Sensorless Non-linear Control Applied to a PMSM Machine Based on New Extended MVT Observer

Observer for nonlinear systems with unknown input using mean value theorem and genetic algorithm

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