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Maxplus algebra and system theory: Where we are and where to go now
 Annu. Rev. Control
, 1999
"... Abstract: More than sixteen years after the beginning of a linear theory for certain discrete event systems in which maxplus algebra and similar algebraic tools play a central role, this paper attempts to summarize some of the main achievements in an informal style based on examples. By comparison ..."
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Cited by 42 (18 self)
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Abstract: More than sixteen years after the beginning of a linear theory for certain discrete event systems in which maxplus algebra and similar algebraic tools play a central role, this paper attempts to summarize some of the main achievements in an informal style based on examples. By comparison with classical linear system theory, there are areas which are practically untouched, mostly because the corresponding mathematical tools are yet to be fabricated. This is the case of the geometric approach of systems which is known, in the classical theory, to provide another important insight to systemtheoretic and controlsynthesis problems, beside the algebraic machinery. A preliminary discussion of geometric aspects in the maxplus algebra and their use for system theory is proposed in the last part of the paper. Résumé: Plus de seize ans après le début d’une théorie linéaire de certains systèmes à événements discrets dans laquelle l’algèbre maxplus et autres outils algébriques assimilés jouent un rôle central, ce papier cherche àdécrire quelques uns des principaux résultats obtenus de façon informelle, en s’appuyant sur des exemples. Par comparaison avec la théorie classique des systèmes linéaires, il existe des domaines pratiquement vierges, surtout en raison du fait que les outils mathématiques correspondants restent à forger. C’est en particulier le cas de l’approche géométrique des systèmes qui, dans la théorie classique, est connue pour apporter un autre regard important sur les questions de théorie des systèmes et de synthèse de lois de commandes àcôté de la machinerie purement algébrique. Une discussion préliminaire sur les aspects géométriques de l’algèbre maxplus et leur utilité pour la théorie des systèmes est proposée dans la dernière partie du papier.
Performance analysis of latencyinsensitive systems
 IEEE Trans. Comput.Aided Design Integr. Circuits Syst
, 2006
"... Abstract—This paper formally models and studies latencyinsensitive systems (LISs) through maxplus algebra. We introduce state traces to model behaviors of LISs and obtain a formally proved performance upper bound achievable by latencyinsensitive design. An implementation of the latencyinsensitive ..."
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Cited by 11 (0 self)
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Abstract—This paper formally models and studies latencyinsensitive systems (LISs) through maxplus algebra. We introduce state traces to model behaviors of LISs and obtain a formally proved performance upper bound achievable by latencyinsensitive design. An implementation of the latencyinsensitive protocol that can provide robust communication through backpressure is also proposed. The intrinsic performance of the proposed implementation is acquired based on state traces. It is also proved that the proposed implementation can always reach the best performance achievable by latencyinsensitive design. Index Terms—Backpressure, latencyinsensitive system, maxplus algebra, performance analysis, state trace.
A PolynomialTime Algorithm for an Equivalence Problem which Arises in Hybrid Systems Theory
 in: Proceedings of the 37th IEEE Conference on Decision and Control
, 1998
"... Piecewise linear (PL) systems provide one systematic approach to discretetime hybrid systems. They blend switching mechanisms with classical linear components, and model arbitrary interconnections of finite automata and linear systems. Tools from automata theory, logic, and related areas of compute ..."
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Cited by 1 (0 self)
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Piecewise linear (PL) systems provide one systematic approach to discretetime hybrid systems. They blend switching mechanisms with classical linear components, and model arbitrary interconnections of finite automata and linear systems. Tools from automata theory, logic, and related areas of computer science and finite mathematics are used in the study of PL systems, in conjunction with linear algebra techniques, all in the context of a "PL algebra" formalism. PL systems are of interest as controllers as well as identification models. Basic questions for any class of systems are those of equivalence, and, in particular, if state spaces are equivalent under a change of variables. This paper studies this statespace equivalence problem for PL systems. The problem was known to be decidable, but its computational complexity was potentially exponential; here it is shown to be solvable in polynomialtime. 1 Introduction Hybrid systems theory has recently become the focus of increased resear...
APolynomialTime Algorithm for an Equivalence Problem which Arises in Hybrid Systems Theory 1
"... Piecewise linear (PL) systems provide one systematic approach to discretetime hybrid systems. They blend switching mechanisms with classical linear components, and model arbitrary interconnections of nite automata and linear systems. Tools from automata theory, logic, and related areas of computer ..."
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Piecewise linear (PL) systems provide one systematic approach to discretetime hybrid systems. They blend switching mechanisms with classical linear components, and model arbitrary interconnections of nite automata and linear systems. Tools from automata theory, logic, and related areas of computer science and nite mathematics are used in the study of PL systems, in conjunction with linear algebra techniques, all in the context of a \PL algebra &quot; formalism. PL systems are of interest as controllers as well as identi cation models. Basic questions for any class of systems are those of equivalence, and, in particular, if state spaces are equivalent under a change of variables. This paper studies this statespace equivalence problem for PL systems. The problem was known to be decidable, but its computational complexitywas potentially exponential� here it is shown to be solvable in polynomialtime. 1
Idempotent Analogue of Resolvent Kernels for a Deterministic Optimal Control Problem
"... Introduction In several places, the use of the semiring (R; min; +) appears to be fundamental in order to apply constructions developed for linear operators to non linear ones. It is well known that the discrete Bellman equation can be treated as linear over appropriate idempotent semirings, and in ..."
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Introduction In several places, the use of the semiring (R; min; +) appears to be fundamental in order to apply constructions developed for linear operators to non linear ones. It is well known that the discrete Bellman equation can be treated as linear over appropriate idempotent semirings, and in the paper, one of the possible directions arising from idempotent analysis is explored: namely, the discretized HamiltonJacobiBellman equation results to be an integral equation and its study can enforce the use of functional analysis methods such as the ones used in the approximation of Volterra equation by means of resolvent kernels. Indeed our method is neither the most general w.r.t idempotent analysis neither conditions which permits to point out this connection are widely assumed in the theory of optimal control, but these permit us to show, that it is possible to apply also in a wider way the analogy between idempotent analysis and functio
An AgentBased Approach to SelfOrganized Production
, 2010
"... The chapter describes the modeling of a material handling system with the production of individual units in a scheduled order. The units represent the agents in the model and are transported in the system which is abstracted as a directed graph. Since the hindrances of units on their path to the de ..."
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The chapter describes the modeling of a material handling system with the production of individual units in a scheduled order. The units represent the agents in the model and are transported in the system which is abstracted as a directed graph. Since the hindrances of units on their path to the destination can lead to inefficiencies in the production, the blockages of units are to be reduced. Therefore, the units operate in the system by means of local interactions in the conveying elements and indirect interactions based on a measure of possible hindrances. If most of the units behave cooperatively (“socially”), the blockings in the system are reduced. A simulation based on the model shows the collective behavior of the units in the system. The transport processes in the simulation can be compared with the processes in a real plant, which gives conclusions about the consequencies for the production based on the superordinate planning.
unknown title
"... www.elsevier.com/locate/tcs A polynomialtime algorithm for checking equivalence under certain semiring congruences motivated bythe statespace isomorphism problem for hybrid systems � Bhaskar DasGuptaa;∗; 1 b; 2 ..."
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www.elsevier.com/locate/tcs A polynomialtime algorithm for checking equivalence under certain semiring congruences motivated bythe statespace isomorphism problem for hybrid systems � Bhaskar DasGuptaa;∗; 1 b; 2
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, 2006
"... System of fuzzy relation equations with inf → composition in semilinear spaces: maximal solutions ..."
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System of fuzzy relation equations with inf → composition in semilinear spaces: maximal solutions