On the boolean minimal realization problem in the max-plus algebra

On the complexity of the boolean minimal realization problem in the max-plus algebra∗

One of the open problems in the max-plus-algebraic system theory for discrete event systems is the minimal realization problem. We consider a simplified version of the general minimal realization problem: the boolean minimal realization problem, i.e., we consider models in which the entries of the system matrices are either equal to the max-plus-algebraic zero element or to the maxplus-algebrai...

On the boolean minimal realization problem in the max-plus algebra: Addendum

On the boolean minimal realization problem in the max-plus algebra

The max-plus algebra is one of the frameworks that can be used to model discrete event systems. One of the open problems in the max-plus-algebraic system theory for discrete event systems is the minimal realization problem. In this paper we present some results for a simplified version of the general minimal realization problem: the boolean minimal realization problem, i.e., we consider models ...

The minimal realization problem in the max-plus algebra

The minimal realization problem in the max-plus algebra, " Chapter 32 in Open Problems in Mathematical Systems and Control Theory

The minimal realization problem in the max-plus algebra: An overview

In this overview report we present known results and open problems in connection with the minimal state space realization problem in the max-plus algebra, which is a framework that can be used to model a class of discrete event systems. 1 Description of the problem Given an n×n matrix A, an n×1 vector b and a 1×n vector c one can construct the sequence gi, i = 1, 2, . . ., where gi is defined b...