On Stability of Uncertain Time-Delay Systems: Robustness Margin for the Inventory Control

Abbou, Rosa; Moussaoui, Charifa; Loiseau, Jean Jacques

doi:10.1016/j.ifacol.2015.09.396

Cited by 5 publications

(6 citation statements)

References 8 publications

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“…Remark 2: Furthermore, we study in this paper a general class of logistic systems with a positive loss factor contrary to [1] and [16] where σ = 0 is considered. Moreover, the model description is completed in this paper where both positive and saturation constraints are considered, contrary to [16] where only saturation constraints are modeled.…”

Section: Comparative Analysis and Discussionmentioning

confidence: 99%

“…The obtained equation is well known by the model reduction or the Artstein's reduction [2]. The state prediction structure was first studied by [18] and used after by [15], [1] and [5]. The basic idea of such a basic prediction principle is to anticipate and fully compensate the system delay θ, by generating a control law that directly uses the corresponding free-delay system (12).…”

Section: Predictive Control Structurementioning

confidence: 99%

“…Proof: The assertions of this theorem are obtained using the Laplace transformation and its properties. Thus, the control input and the system output dynamics defined respectively by (10) and (1), are expressed based on the prediction dynamics given by (12) with z(0) = y(0) + w, as follows:…”

Section: Input-output Reachable Boundsmentioning

confidence: 99%

See 2 more Smart Citations

Predictive Feedback Control for Inventory Systems Subject to Delays and Constraints

Farraa¹,

Abbou²,

Loiseau³

2023

IEEE Trans. Automat. Contr.

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In this paper, we discuss the inventory regulation problem of a logistic system composed of a production unit and inventory unit. The production system is characterized by a constant lead time, and the storage unit presents fixed losses due to perishable products. In this study, the system is subject to finite production resources, limited storage capacities, and the customer demands are uncertain in a given range. We address a control strategy to the input time delay system that is subject to positive and saturation constraints and to bounded disturbances. We apply a linear prediction feedback control strategy, in order to stabilize the closed-loop system and to fulfill the system constraints, so that necessary and sufficient conditions for the existence of an admissible control law are formulated.

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Section: Comparative Analysis and Discussionmentioning

confidence: 99%

Section: Predictive Control Structurementioning

confidence: 99%

See 1 more Smart Citation

Predictive Feedback Control for Inventory Systems Subject to Delays and Constraints

Farraa¹,

Abbou²,

Loiseau³

2023

IEEE Trans. Automat. Contr.

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“…(1978). The basic issue is to compensate the time delay by generating a control law that uses directly the corresponding delay-free system, as developed in Bou Farraa, B. et al (2018) and Abbou et al (2015). However, the system delay presents some uncertainties that are expressed by the following range:…”

Section: Inventory Control Structurementioning

confidence: 99%

“…Through the years, different studies were based on differential equations and feedback structures, to model and control production systems, see Ignaciuk P., and Bartoszewicz, A. (2011), Abbou et al (2015) and Bou Farraa, B. et al (2018). The first contribution of this work provides a robust control law which guarantee the stability of the closedloop system, using a feedback-predictor control structure.…”

Section: Introductionmentioning

confidence: 99%

Robust stabilization of an elementary logistic system with an input delay

2020

Self Cite

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In this paper, we are interested in the robustness analysis of an elementary logistic system having a fixed loss factor on the inventory level and uncertainties on the production delay. The problem is treated in control theory domain, where the model is considered as an input time delay system characterized by positivity and saturation constraints, and an external disturbance. Indeed, we apply a prediction state feedback control strategy using an affine control law, where the prediction of the future inventory level is based on a delay estimation of the delay uncertainty. Hence, the objective of the study is to quantify the impact of the uncertainty induced by this estimation on the performance of the controlled system. First, we use a frequency-domain technique to identify the robust stability condition in the set of parameters. In particular, we specify the range of the delay deviation such that the closed-loop system stability is guaranteed. Then, we move on to define the input-output flow variations that allows to check the system constraints, based on the invariance properties. Finally, a comparative simulation is provided to highlight the advantages of this study.

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On Inventory Control For Perishable Inventory Systems Subject To Uncertainties On Customer Demands

et al. 2017

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On Stability of Uncertain Time-Delay Systems: Robustness Margin for the Inventory Control

Cited by 5 publications

References 8 publications

Predictive Feedback Control for Inventory Systems Subject to Delays and Constraints

Predictive Feedback Control for Inventory Systems Subject to Delays and Constraints

Robust stabilization of an elementary logistic system with an input delay

On Inventory Control For Perishable Inventory Systems Subject To Uncertainties On Customer Demands

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