Robust Interval Observer for Systems Described by the Fornasini–Marchesini Second Model

Chevet, Thomas; Rauh, Andreas; Dinh, Thach Ngoc; Marzat, Julien; Raïssi, Tarek

doi:10.1109/lcsys.2021.3136762

Cited by 10 publications

(4 citation statements)

References 31 publications

(43 reference statements)

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“…which accounts for a non-zero ellipsoid midpoint with z k , Φ, and p defined according to ( 5), (7), and ( 8). Inflate the ellipsoid bound described by the shape matrix (11) according to…”

Section: Covariance Prediction Using Ellipsoidal Calculusmentioning

confidence: 99%

“…Examples, in which nonlinear applications are taken into consideration by data-driven learning observer approaches can be found in [9], [10]. Recently, the authors have published a related work on the interval observer design for 2D systems described in the form of the Fornasini-Marchesini second model [11], where the focus was on evaluating and verifying stability criteria in the form of LMIs in combination with the optimization of the peak-to-peak norm to reduce the effects of measurement errors on the state estimates. In addition, a KF-like realization of ILO was published in [12].…”

Section: Introductionmentioning

confidence: 99%

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Robust Iterative Learning Observers Based on a Combination of Stochastic Estimation Schemes and Ellipsoidal Calculus

Rauh

Chevet

Dinh

et al. 2022

2022 25th International Conference on Information Fusion (FUSION)

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The state estimation of repetitive processes with periodically repeated trajectories can be interpreted as the dual task of iterative learning control design. While the latter has been widely investigated over the last two decades, only few approaches exist for the design of iterative learning observers. However, the exploitation of the knowledge about periodically repeated trajectories, which occur among others in pick and place tasks in robotics as well as in charging and discharging of batteries, offers the opportunity to enhance the estimation accuracy from one execution of the control task to the next. In this paper, we generalize a linear stochastic approach for iterative learning state estimation, inspired by the Kalman filter in terms of a minimization of the estimation error covariance, to the class of models with bounded parameter uncertainty and to nonlinear ones that can be represented by means of quasi-linear discrete-time state-space representations. To solve this task, a novel combination of set-valued ellipsoidal state enclosure techniques with the aforementioned stochastic iterative learning state estimator is presented and visualized for a quasilinear model of the charging/discharging dynamics of Lithium-Ion batteries.

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“…which accounts for a non-zero ellipsoid midpoint with z k , Φ, and p defined according to ( 5), (7), and ( 8). Inflate the ellipsoid bound described by the shape matrix (11) according to…”

Section: Covariance Prediction Using Ellipsoidal Calculusmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Iterative Learning Observers Based on a Combination of Stochastic Estimation Schemes and Ellipsoidal Calculus

Rauh

Chevet

Dinh

et al. 2022

2022 25th International Conference on Information Fusion (FUSION)

Self Cite

View full text Add to dashboard Cite

show abstract

“…For nonlinear applications, data-driven learning observer approaches were derived in [9], [10]. Recently, a related topic in the frame of an interval observer design for 2D systems described in the form of the Fornasini-Marchesini second model was derived in [11], where the focus was on evaluating and verifying stability criteria in the form of LMIs in combination with the optimization of the peak-to-peak norm to reduce the effects of measurement errors on the state estimates.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Design Approach for Iterative Learning Observers for the Estimation of Periodically Recurring Trajectories and Disturbances

Rauh

Chevet²,

Dinh

et al. 2022

2022 European Control Conference (ECC)

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Many repetitive control problems are characterized by the fact that disturbances have the same effect in each successive execution of the same control task. Such disturbances comprise the lumped representation of unmodeled parts of the open-loop system dynamics, a systematic model-mismatch or, more generally, deterministic yet unknown uncertainty. In such cases, well-known strategies for iterative learning control are based on enhancing the system behavior not only by exploiting data gathered during a single execution of the task but also using information from previous executions. The corresponding dual problem, namely, iterative learning state and disturbance estimation has not yet received the same amount of attention. However, it is obvious that improved estimates for the aforementioned states and disturbances which periodically occur in each execution will be a means to achieve an improved accuracy and, therefore, in future work also to optimize the control accuracy. In this paper, we present a joint design procedure for observer gains in two independent dimensions, a gain for processing information in the temporal domain during a single execution of the task (also named trial) and a gain for learning in the iteration domain (i.e., from trial to trial).

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“…Nevertheless, the application of interval observers on chaotic synchronization in secure transmission of information systems remains an open problem as there is hardly a very few works that address this problem [1], [2], [7], [12].…”

Section: Introductionmentioning

confidence: 99%

Disturbed chaotic system synchronization via nonlinear robust interval state observers

Khemiri

Tlili

2022

Preprint

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In this paper, a nonlinear interval state observer design method is synthesized for chaos synchronization between master (drive) and slave (response) systems based on the Luenberger-type observer. The stability study, analyzed with Lyapunov’s approach, is formulated in terms of linear matrix inequalities (LMIs) and subsequently to calculate the observation gain matrix. The stability of the designed state observer is analyzed within the Lyapunov approach and the LMI paradigm. Moreover, the nonlinear interval observer, comprising the lower and upper bound state observers, is used for the state reconstruction of nonlinear perturbed chaotic sys- tems subject to unknown but bounded external disturbances. The effi- ciency and high performances of the aforementioned state observer-based synchronization technique are demonstrated by a large study of numeri- cal simulation for the state synchronization of perturbed unified chaotic systems. keywords : State synchronization Nonlinear perturbed chaotic sys- tems Nonlinear interval observer Lyapunov approach LMI paradigm

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Robust Interval Observer for Systems Described by the Fornasini–Marchesini Second Model

Cited by 10 publications

References 31 publications

Robust Iterative Learning Observers Based on a Combination of Stochastic Estimation Schemes and Ellipsoidal Calculus

Robust Iterative Learning Observers Based on a Combination of Stochastic Estimation Schemes and Ellipsoidal Calculus

A Stochastic Design Approach for Iterative Learning Observers for the Estimation of Periodically Recurring Trajectories and Disturbances

Disturbed chaotic system synchronization via nonlinear robust interval state observers

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