Observer-Based Controllers for Max-Plus Linear Systems

Hardouin, Laurent; Shang, Ying; Maia, Carlos Andrey; Cottenceau, Bertrand

doi:10.1109/tac.2016.2604562

Cited by 23 publications

(12 citation statements)

References 29 publications

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“…An advantage of this approach is that the already existing tools for standard TEGs in the dioid M ax in [[γ, δ]] can be applied to the more general class of TEGsPS. Based on these results, many control concepts already introduced for TEGs, such as model-reference control Maia et al (2003), observer based control Hardouin et al (2017), etc. can be generalized for TEGsPS.…”

Section: Resultsmentioning

confidence: 99%

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Model Decomposition of Timed Event Graphs under Partial Synchronization in Dioids

et al. 2018

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Timed Event Graphs (TEGs) are a graphical model for decision free and time-invariant Discrete Event Systems (DESs). To express systems with time-variant behaviors, a new form of synchronization, called partial synchronization (PS), has been introduced for TEGs. Unlike exact synchronization, where two transitions t 1 , t 2 can only fire if both transitions are simultaneously enabled, PS of transition t 1 by transition t 2 means that t 1 can fire only when transition t 2 fires, but t 1 does not influence the firing of t 2 . Under some assumptions, we can show that the dynamic behavior of a TEG under PS can be decomposed into a time-variant and a time-invariant part. The time-invariant part can be interpreted as a standard TEG. Moreover, it is shown that the tools introduced for standard TEGs can be used to analyze the overall system.

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Section: Resultsmentioning

confidence: 99%

“…Moreover, based on M ax in [[γ, δ]], methods for performance evaluation and controller synthesis have been introduced for TEGs, e.g. Gaubert and Klimann (1991); Maia et al (2003); Hardouin et al (2017). In Hardouin et al (2009) Fig.…”

Section: Subdioids Of T [[γ]]mentioning

confidence: 99%

Model Decomposition of Timed Event Graphs under Partial Synchronization in Dioids

et al. 2018

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“…Observer design for max-plus linear systems is considered in Hardouin et al (2010) and Hardouin et al (2017). Stochastic filtering of max-plus linear systems with bounded disturbances is discussed in Santos-Mendes et al (2019).…”

Section: Identification and Verificationmentioning

confidence: 99%

Analysis and control of max-plus linear discrete-event systems: An introduction

Schutter

Boom

et al. 2019

Discrete Event Dyn Syst

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The objective of this paper is to provide a concise introduction to the max-plus algebra and to max-plus linear discrete-event systems. We present the basic concepts of the max-plus algebra and explain how it can be used to model a specific class of discreteevent systems with synchronization but no concurrency. Such systems are called max-plus linear discrete-event systems because they can be described by a model that is "linear" in the max-plus algebra. We discuss some key properties of the max-plus algebra and indicate how these properties can be used to analyze the behavior of max-plus linear discrete-event systems. Next, some control approaches for max-plus linear discrete-event systems, including residuation-based control and model predictive control, are presented briefly. Finally, we discuss some extensions of the max-plus algebra and of max-plus linear systems. Keywords Max-plus linear systems • Max-plus algebra • Analysis of discrete-event systems • Model-based control of max-plus linear systems • Residuation-based control • Model predictive control • Survey

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“…Suppose that the transmission time from E j to R i may vary randomly between b i and b i , the processing time of R i may vary randomly between t i and t i , and at the same time, the processing result of R i is required to be output at any specified time between i and i , where i ∈  and ∈  . Then, in system (12),…”

Section: Application In Data Transmission Systemsmentioning

confidence: 99%

“…Max-plus linear systems, [1][2][3] which have maximization and addition as their basic operations, describe a class of dynamical systems with synchronization but no concurrency, although such systems are generally nonlinear descriptions in conventional algebra. Many effective methods are available for assessing the characteristics and performances of max-plus linear systems such as periodicity and stability, [4][5][6][7][8][9] controllability and observability, [10][11][12] and optimization problems. [13][14][15][16][17] Applications of max-plus linear systems often arise in the context of manufacturing plants, traffic scheduling, queuing systems, etc.…”

Section: Introductionmentioning

confidence: 99%

Optimal input design for uncertain max‐plus linear systems

Wang

Tao

Yan

2018

Intl J Robust & Nonlinear

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Summary This paper investigates the optimal input design for uncertain max‐plus linear systems whose parameters are only known to belong to certain intervals. The exact interval input is introduced to minimize the regulating range of the input that ensures that the system can output at any specified value in the desired interval regardless of how the parameters vary in certain ranges. The optimal input design for uncertain max‐plus linear systems is formulated as an optimal control problem that finds the maximum element of the set of exact interval inputs with respect to the order of max‐plus interval vectors. This paper also considers the optimal approximate interval input of an uncertain max‐plus linear system that has no exact interval input. A polynomial algorithm is developed to find the optimal interval input and optimal approximate interval input of an uncertain max‐plus linear system. A data transmission system with parameter perturbations is employed as an example to demonstrate how the proposed results work in practical applications.

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Observer-Based Controllers for Max-Plus Linear Systems

Cited by 23 publications

References 29 publications

Model Decomposition of Timed Event Graphs under Partial Synchronization in Dioids

Model Decomposition of Timed Event Graphs under Partial Synchronization in Dioids

Analysis and control of max-plus linear discrete-event systems: An introduction

Optimal input design for uncertain max‐plus linear systems

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