Unknown input interval observers for discrete-time linear switched systems

Marouani, Ghassen; Dinh, Thach Ngoc; Raïssi, Tarek; Wang, Xin; Messaoud, Hassani

doi:10.1016/j.ejcon.2020.09.004

Cited by 24 publications

(10 citation statements)

References 27 publications

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“…The property of cooperativity only holds for a quite restricted class of system models (e.g., thermo-fluidic ones) after a first-principle modeling. So, simulation and state estimation techniques that rely on cooperativity often need to be implemented in combination with an additional change of coordinates (Marouani et al, 2021;Rauh and Kersten, 2021). This change of coordinates is on purpose avoided in the current paper due to the following reasons: Especially for uncertain systems, such changes of coordinates are non-trial to find (if they exist at all) and they typically lead to overestimation that can be avoided by the use of the ellipsoidal enclosure technique derived in this paper.…”

Section: Introductionmentioning

confidence: 99%

An Ellipsoidal Predictor–Corrector State Estimation Scheme for Linear Continuous-Time Systems With Bounded Parameters and Bounded Measurement Errors

Rauh

Rohou

Jaulin

2022

Front. Control Eng.

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For linear time-invariant dynamic systems with exactly known coefficients of their system matrices for which measurements with bounded errors are available at discrete time instants, an optimal polygonal state estimation scheme was recently published. This scheme allows for tightly enclosing all possible state trajectories in presence of uncertain, but bounded, system inputs which may be varying arbitrarily within in their bounds. Moreover, this approach is also capable of accounting for uncertainty related to the measurement time instants. However, the drawback of this polygonal technique is its rapidly increasing complexity for larger system dimensions. For that reason, the polygonal state enclosures are replaced by a computationally less expensive, but nearly optimal, ellipsoidal enclosure technique in this paper. Numerical simulations for representative benchmark examples focusing both on applications with precisely known and uncertain parameters conclude this contribution.

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Section: Introductionmentioning

confidence: 99%

An Ellipsoidal Predictor–Corrector State Estimation Scheme for Linear Continuous-Time Systems With Bounded Parameters and Bounded Measurement Errors

Rauh

Rohou

Jaulin

2022

Front. Control Eng.

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“…Due to the practical relevance of the problems the UIOs address , there are several contributions to this field in the literature (e.g., [3]) While the early works on UIOs were initially focused on linear systems [4], significant research effort has been dedicated to their design for several classes of nonlinear systems, namely LPV systems [5], [6], discrete Fuzzy systems [7] or bilinear continuous Fuzzy systems, with single input [8], [9] or multiple inputs [10]. Furthermore, a new approach as the interval UIOs have been recently developed, as shown in [11] for systems with non-noisy outputs and in [12], [13] for systems with noisy outputs. It must to be noticed that the aforementioned classes of systems are amenable to the use of convex approaches for both control and observation (see [14]).…”

Section: Introductionmentioning

confidence: 99%

“…power converters, as DC-DC or AC-DC ones). Moreover, measurement noise and model uncertainty are rarely taken into account, with some notable exception as [12], [13] and [10]. In [12] and [13], the interval observer is first designed, and a bound on the error is given a posteriori, with the consequence that the sensitivity to noise is not optimized.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, measurement noise and model uncertainty are rarely taken into account, with some notable exception as [12], [13] and [10]. In [12] and [13], the interval observer is first designed, and a bound on the error is given a posteriori, with the consequence that the sensitivity to noise is not optimized. To the best of our knowledge, the synthesis of an observer gain that minimizes the impact of noise and uncertainty for either LPV or bilinear systems has not been conducted.…”

Section: Introductionmentioning

confidence: 99%

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Robust Observer synthesis for Bilinear Parameter Varying system

Etienne¹,

Langueh²,

Karkaba³

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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In the present paper, sufficient conditions for the synthesis of robust Unknown Input Observers (UIOs) are proposed for a class of nonlinear systems, both in continuous and discrete time. The considered class is general enough to contain bilinear systems as well as Linear Parameter-Varying (LPV) systems with no parameter variation on the output matrix. The proposed conditions are numerically tractable, and are expressed in terms of Linear Matrix Inequalities (LMIs) or Linear Matrix Equalities (LMEs). Furthermore, the gain synthesis problem is shown to be formulated as a convex optimisation one, directly enabling the minimization of the influence of noisy measurements and model uncertainty. Simulations on energy systems are provided to illustrate the proposed methodologies.

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“…The interval observer was designed for switched systems by the monotone theory for the first time [13]. By using the coordinate transformation method, the interval observer was designed for switched systems with unknown input [21], and then the optimal interval observer design as well as fault estimation for T-S fuzzy systems were both studied in [12]. Besides, there also exists many other works on interval observer for switched systems such as [7,9].…”

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confidence: 99%

Interval estimation methods of fault estimation for discrete-time switched systems

Huang¹,

Zhang²,

Chen³

et al. 2023

JIMO

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<p style='text-indent:20px;'>This paper investigates the fault estimation problem for discrete-time switched systems. Firstly, the sensor fault is regarded as an augmented state, and then the original system is converted into a singular system. After that, based on the obtained singular system, a robust augmented state observer is designed using <inline-formula><tex-math id="M1">\begin{document}$ L_{\infty} $\end{document}</tex-math></inline-formula> technique. Given above robust augmented state observer, an interval observer based on the zonotope method is established to complete the fault interval estimation. Finally, a circuit system is simulated to illustrate the efficiency of the proposed method.</p>

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Unknown input interval observers for discrete-time linear switched systems

Cited by 24 publications

References 27 publications

An Ellipsoidal Predictor–Corrector State Estimation Scheme for Linear Continuous-Time Systems With Bounded Parameters and Bounded Measurement Errors

An Ellipsoidal Predictor–Corrector State Estimation Scheme for Linear Continuous-Time Systems With Bounded Parameters and Bounded Measurement Errors

Robust Observer synthesis for Bilinear Parameter Varying system

Interval estimation methods of fault estimation for discrete-time switched systems

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