Max–plus matrix method and cycle time assignability and feedback stabilizability for min–max–plus systems

Tao, Yuegang; Liu, Shuai; Mu, Xiaomin

doi:10.1007/s00498-012-0098-7

Cited by 5 publications

(6 citation statements)

References 36 publications

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“…Other related work on modeling and analysis different types of systems using max-plus algebra can be found in Declerck (2011), Shang and Sain (2009), Tao et al (2013), Addad et al (2012), Lu et al (2012), Takahashi (2012), Nait-Sidi-Moh et al (2009), Addad et al (2011), Su andWoeginger (2011), Ferreira Cândido et al (2018), and Adzkiya et al (2015).…”

Section: Modeling and Performance Analysismentioning

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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Section: Modeling and Performance Analysismentioning

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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“…Based on such a canonical form, some interesting results with profound significance have been obtained in max-min systems, such as the duality theorem [7] and constructive fixed point theorem [5], and some control problems are also considered (see e.g. [2,16,17]). It is known that any Boolean function can be put into a minterm canonical form [15].…”

Section: Introductionmentioning

confidence: 99%

Reconstruct the Logical Network from the Transition Matrix

Wang,

Tao

2017

Preprint

Self Cite

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Reconstructing the logical network from the transition matrix is benefit for learning the logical meaning of the algebraic result from the algebraic representation of a BN. And so far there has no method to convert the matrix expression back to the logic expression for a BN with an arbitrary topology structure. Based on the canonical form and Karnaugh map, we propose a method for reconstructing the logical network from the transition matrix of a Boolean network in this paper.

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“…Min-max systems are nonlinear extensions of max-plus systems. There has been increasing interest in the control of min-max systems due to its significance both in theory and applications and much closely related work has been done [1][2][3][4][5][6][7][8][9]. De Schutter and van den Boom [1] introduced the model predictive control framework into min-max systems.…”

Section: Introductionmentioning

confidence: 99%

“…Necoara et al [2] extended the classical min-max model predictive control framework to more general max-min-plus-scaling systems and proposed both open-loop and disturbance feedback approaches. Chen et al [3][4][5][6] introduced the feedback control into min-max systems and investigated reachability, observability, cycle time assignment and state and output feedback stabilization.…”

Section: Introductionmentioning

confidence: 99%

“…This paper investigates min-max systems with min-max inputs and outputs and focuses on the cycle time assignability with respect to an output feedback. These systems are nonlinear extensions of the systems presented in [3][4][5][6] and more complex than them. It is pointed out that the closed loop max-plus projection systems in such systems have strict position matching requirements.…”

Section: Introductionmentioning

confidence: 99%

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Output Feedback Assignability for Nonlinear Min-Max Systems

Wei

Zhu

Yin

et al. 2011

AMR

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This paper investigates the output feedback cycle time assignability of the min-max systems which are more complex than the systems studied in recent years. Max-plus projection representation for the closed-loop system with min-max output feedback is introduced. The coloring graph is presented and applied to analyze the structure of systems effectively. The necessary and sufficient criterion for the output feedback cycle time assignability is established which is an extension of the results studied before. The methods are constructive in nature.

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Max–plus matrix method and cycle time assignability and feedback stabilizability for min–max–plus systems

Cited by 5 publications

References 36 publications

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

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

Reconstruct the Logical Network from the Transition Matrix

Output Feedback Assignability for Nonlinear Min-Max Systems

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