Duality and interval analysis over idempotent semirings
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TLDR
In this paper, the authors considered semirings with an idempotent addition and proved sufficient conditions for the existence of a non-linear projector in the solution set, and extended these results to semirungs of intervals.About:
This article is published in Linear Algebra and its Applications.The article was published on 2012-11-15 and is currently open access. It has received 23 citations till now. The article focuses on the topics: Idempotent matrix & Duality (order theory).read more
Citations
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Observer Design for (max,+) linear systems
TL;DR: In this article, the state estimation for max-plus linear systems is carried out following the ideas of the observer method for classical linear systems, where the system matrices are assumed to be known, and the observation of the input and of the output is used to compute the estimated state.
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Conditional reachability of uncertain Max Plus Linear systems
Renato Markele Ferreira Cândido,Renato Markele Ferreira Cândido,Laurent Hardouin,Mehdi Lhommeau,Rafael Santos Mendes,Rafael Santos Mendes +5 more
TL;DR: Using the results on the reachability analysis of uMPL systems, the conditional reachability problem is solved, herein defined as the support calculation of the probability density function involved in the stochastic filtering problem.
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Optimal control for timed event graphs under partial synchronization
TL;DR: Under some assumptions, optimal control, already available for classical TEGs, is extended to T EGs under partial synchronization: optimal control has to fire when transition T1 fires, but transition T* is not influenced by transition T.
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Analysis of Cycle Time in Interval P-Time Event Graphs in Dioid Algebras
Pavel Špaček,Jan Komenda +1 more
TL;DR: In this article, a new approach to the modeling and analysis of cycle times in interval P-time event graphs based on dual linear representations in the (max,+) and (min,+) semirings is proposed.
References
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Book
Methods and applications of interval analysis
TL;DR: Finite representations Finite evaluation Finite convergence Computable sufficient conditions for existence and convergence Safe starting regions for iterative methods.
Journal ArticleDOI
Synchronization and Linearity: An Algebra for Discrete Event Systems
TL;DR: This book proposes a unified mathematical treatment of a class of 'linear' discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints, which is shown to parallel the classical linear system theory in several ways.
Book
Applied interval analysis : with examples in parameter and state estimation, robust control and robotics
TL;DR: In this paper, the authors present a set-based approach for estimating the length of a set with respect to a set of set operators and the number of sets in the set.