Linear systems in (max,+) algebra
نویسندگان
چکیده
Proceedings of the 29th Conference on Decision and Control Honolulu, Dec. 1990 Abstract In this paper, we study the general system of linear equations in the algebra. We introduce a symmetrization of this algebra and a new notion called balance which generalizes classical equations. This construction results in the linear closure of the algebra in the sense that every nondegenerate system of linear balances has a unique solution given by Cramer’s rule.
منابع مشابه
Max-Plus algebra on tensors and its properties
In this paper we generalize the max plus algebra system of real matrices to the class of real tensors and derive its fundamental properties. Also we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverses of tensors is characterized.
متن کاملMax-plus algebra and max-plus linear discrete event systems: An introduction
We provide an introduction to the max-plus algebra and explain how it can be used to model a specific class of discrete event 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 thes...
متن کاملThe QR Decomposition and the Singular Value Decomposition in the Symmetrized Max-Plus Algebra Revisited
This paper is an updated and extended version of the paper “The QR decomposition and the singular value decomposition in the symmetrized max-plus algebra” (by B. De Schutter and B. De Moor, SIAM Journal on Matrix Analysis and Applications, vol. 19, no. 2, pp. 378–406, April 1998). The max-plus algebra, which has maximization and addition as its basic operations, can be used to describe and anal...
متن کاملThe Qr Decomposition and the Singularvalue Decomposition in the Symmetrizedmax - plus Algebrab
The max-plus algebra has maximization and addition as basic operations, and can be used to model a certain class of discrete event systems. In contrast to linear algebra and linear system theory many fundamental problems in the max-plus algebra and in max-plus-algebraic system theory still need to be solved. In this paper we discuss max-plus-algebraic analogues of some basic matrix decompositio...
متن کاملTropical linear algebra with the Łukasiewicz T-norm
The max-Łukasiewicz semiring is defined as the unit interval [0, 1] equipped with the arithmetics “a + b” = max(a, b) and “ab” = max(0, a + b− 1). Linear algebra over this semiring can be developed in the usual way. We observe that any problem of the max-Łukasiewicz linear algebra can be equivalently formulated as a problem of the tropical (max-plus) linear algebra. Based on this equivalence, w...
متن کاملMax-algebra: the linear algebra of combinatorics?
Let a ⊕ b = max(a, b), a ⊗ b = a + b for a, b ∈ R := R ∪ {−∞}. By max-algebra we understand the analogue of linear algebra developed for the pair of operations (⊕,⊗) extended to matrices and vectors. Max-algebra, which has been studied for more than 40 years, is an attractive way of describing a class of nonlinear problems appearing for instance in machinescheduling, information technology and ...
متن کامل