A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to...A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to discrete event systems in order to represent its states evolution where the timing at which the state changes is taken into consideration. One of the most important performance issues to be considered in a discrete event system is its stability. Lyapunov theory provides the required tools needed to aboard the stability and stabilization problems for discrete event systems modeled with timed Petri nets whose mathematical model is given in terms of difference equations. By proving stability one guarantees a bound on the discrete event systems state dynamics. When the system is unstable, a sufficient condition to stabilize the system is given. It is shown that it is possible to restrict the discrete event systems state space in such a way that boundedness is achieved. However, the restriction is not numerically precisely known. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra, which is assigned to the timed Petri net graphical model.展开更多
The eigenvectors of a fuzzy matrix correspond to steady states of a complex discrete-events system, characterized by the given transition matrix and fuzzy state vectors. The descriptions of the eigenspace for matrices...The eigenvectors of a fuzzy matrix correspond to steady states of a complex discrete-events system, characterized by the given transition matrix and fuzzy state vectors. The descriptions of the eigenspace for matrices in the max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra have been presented in previous papers. In this paper, we investigate the monotone eigenvectors in a max-T algebra, list some particular properties of the monotone eigenvectors in max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra, respectively, and illustrate the relations among eigenspaces in these algebras by some examples.展开更多
This research develops a solution method for project scheduling represented by a max-plus-linear (MPL) form. Max-plus-linear representation is an approach to model and analyze a class of discrete-event systems, in whi...This research develops a solution method for project scheduling represented by a max-plus-linear (MPL) form. Max-plus-linear representation is an approach to model and analyze a class of discrete-event systems, in which the behavior of a target system is represented by linear equations in max-plus algebra. Several types of MPL equations can be reduced to a constraint satisfaction problem (CSP) for mixed integer programming. The resulting formulation is flexible and easy-to-use for project scheduling;for example, we can obtain the earliest output times, latest task-starting times, and latest input times using an MPL form. We also develop a key method for identifying critical tasks under the framework of CSP. The developed methods are validated through a numerical example.展开更多
文摘A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to discrete event systems in order to represent its states evolution where the timing at which the state changes is taken into consideration. One of the most important performance issues to be considered in a discrete event system is its stability. Lyapunov theory provides the required tools needed to aboard the stability and stabilization problems for discrete event systems modeled with timed Petri nets whose mathematical model is given in terms of difference equations. By proving stability one guarantees a bound on the discrete event systems state dynamics. When the system is unstable, a sufficient condition to stabilize the system is given. It is shown that it is possible to restrict the discrete event systems state space in such a way that boundedness is achieved. However, the restriction is not numerically precisely known. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra, which is assigned to the timed Petri net graphical model.
文摘The eigenvectors of a fuzzy matrix correspond to steady states of a complex discrete-events system, characterized by the given transition matrix and fuzzy state vectors. The descriptions of the eigenspace for matrices in the max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra have been presented in previous papers. In this paper, we investigate the monotone eigenvectors in a max-T algebra, list some particular properties of the monotone eigenvectors in max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra, respectively, and illustrate the relations among eigenspaces in these algebras by some examples.
文摘This research develops a solution method for project scheduling represented by a max-plus-linear (MPL) form. Max-plus-linear representation is an approach to model and analyze a class of discrete-event systems, in which the behavior of a target system is represented by linear equations in max-plus algebra. Several types of MPL equations can be reduced to a constraint satisfaction problem (CSP) for mixed integer programming. The resulting formulation is flexible and easy-to-use for project scheduling;for example, we can obtain the earliest output times, latest task-starting times, and latest input times using an MPL form. We also develop a key method for identifying critical tasks under the framework of CSP. The developed methods are validated through a numerical example.
