By Luca Benvenuti, Alberto de Santis, Lorenzo Farina
The court cases of the 1st Multidisciplinary overseas Symposium on confident platforms idea and purposes (POSTA 2003) held in Rome, Italy, August 28-30, 2003. optimistic structures are platforms within which the suitable variables think nonnegative values. those platforms are very common in purposes the place variables characterize confident amounts reminiscent of populations, items, funds, time, facts packets flowing in a community, densities of chemical species, possibilities, and so on. the purpose of the symposium was once to hitch jointly researchers operating within the various components relating to optimistic platforms comparable to telecommunications, financial system, biomedicine, chemistry and physics for you to offer a multidisciplinary discussion board the place they've got the chance to switch principles and examine leads to a unifying framework.
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Simon. Recognizable sets with multiplicities in the tropical semiring. In MFCS’88, number 324 in LNCS. Springer, 1988. 33. E. Wagneur. Moduloids and pseudomodules. 1. dimension theory. , 98:57–73, 1991. 34. W. Wonham. Linear multivariable control: a geometric approach. Springer, 1985. fr Abstract. We consider the modelling of urban bus networks in dioid algebras. In particular, we show that their dynamic behavior can be modeled by a Min-Max recursive equation. 1 Introduction The evolution of a class of Discrete Event Dynamic System (DEDS), viz those which involve synchronization phenomena, can be described by linear models provided that a particular algebraic structure, called dioid or idempotent semi-ring, is used.
Prou and E. Wagneur. Controllability in the max-algebra. Kybernetika (Prague), 35(1):13–24, 1999. 32. I. Simon. Recognizable sets with multiplicities in the tropical semiring. In MFCS’88, number 324 in LNCS. Springer, 1988. 33. E. Wagneur. Moduloids and pseudomodules. 1. dimension theory. , 98:57–73, 1991. 34. W. Wonham. Linear multivariable control: a geometric approach. Springer, 1985. fr Abstract. We consider the modelling of urban bus networks in dioid algebras. In particular, we show that their dynamic behavior can be modeled by a Min-Max recursive equation.
3 Max-plus reachable spaces Let us know consider the max-plus linear system x(k) = Ax(k − 1) ⊕ Bu(k), y(k) = Cx(k), q×1 x(k) ∈ Zn×1 max , y(k) ∈ Zmax , (2) where A, B, C are matrices with entries in Zmax , of dimension n × n, n × p, and q × n, respectively. We know from [3] that (2) represents the behavior of a class of discrete event systems called Timed Event Graphs. We call reachable space in time k, and denote by Rk , the set of states x(k) reachable from the initial state x(0) = , where denotes the zero vector.