On max-plus linear dynamical system theory: The regulation problem

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• 作者：Vinicius Mariano Gonç ; alves^a ; ^{mariano@cpdee.ufmg.br}Author Vitae ; Carlos Andrey Maia^a ; ^{maia@cpdee.ufmg.br}Author Vitae ; Laurent Hardouin^b ; ^{laurent.hardouin@univ-angers.fr}Author Vitae
• 关键词：Max-plus algebra ; Tropical algebra ; Timed-event graphs ; Geometric control
• 刊名：Automatica
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：75
• 期：Complete
• 页码：202-209
• 全文大小：625 K
• 卷排序：75

文摘

A class of timed discrete event systems can be modeled by using Timed-Event Graphs, a class of timed Petri nets that can have its firing dynamic described by using an algebra called “Max-plus algebra”. For this kind of systems it may be desirable to enforce some timing constraints in steady state. In this paper, this problem is called a “max-plus regulation problem”. In this context we show a necessary condition for solving these regulation problems and in addition that this condition is sufficient for a large class of problems. The obtained controller is a simple linear static state feedback and can be computed using efficient pseudo-polynomial algorithms. Simulation results will illustrate the applicability of the proposed methodology.