This book concerns the use of dioid algebra as (max, +) algebrato treat the synchronization of tasks expressed by the maximum ofthe ends of the tasks conditioning the beginning of another task- a criterion of linear programming. A classical example isthe departure time of a train which should wait for the arrival ofother trains in order to allow for the changeover ofpassengers.
The content focuses on the modeling of a class of dynamic systemsusually called "discrete event systems" where thetiming of the events is crucial. Events are viewed as suddenchanges in a process which is, essentially, a man-made system, suchas automated manufacturing lines or transportation systems. Itsmain advantage is its formalism which allows us to clearly describecomplex notions and the possibilities to transpose theoreticalresults between dioids and practical applications.
Auflage
Sprache
Verlagsgruppe
Produkt-Hinweis
Dateigröße
ISBN-13
978-1-118-57862-9 (9781118578629)
Schweitzer Klassifikation
Chapter 1 Introduction
General introduction
History and three mainstays
Scientific context
Dioids
Petri nets
Time and algebraic models
Organization of the book
Chapter 2 Consistency
Introduction
Models
Physical point of view
Objectives
Preliminaries
Models and principle of the approach
P-time event graphs
Dater form
Principle of the approach (example)
Analysis in the "static" case
"Dynamic" model
Extremal acceptable trajectories by series of matrices
Lowest state trajectory
Greatest state trajectory
Consistency
Maximal horizon of temporal consistency
Date of the first token deaths
Computational complexity
Conclusion
Chapter 3 Cycle Time
Objectives
Problem without optimization
Matrix expression of a P-time event graph
Matrix expression of P-time event
graphs with interdependent residence durations
General form Ax <= b
Existence of a -periodic behavior
Conclusion
Chapter 4 Control with Specifications
Introduction
Time interval systems
(min, max, +) algebraic models
Timed event graphs
P-time event graphs
Time stream event graphs
Control synthesis
Problems
Pedagogical example: education system
Algebraic models
Fixed-point approach
Fixed-point formulation
Existence
Structure
Algorithm
Models
Fixed-point formulation
Optimal control with specifications
Initial conditions
Conclusion
Chapter 5 Online Aspect of Predictive Control
Introduction
Problem
Specific characteristics
Control without desired output (problem)
Objective
Example
Trajectory description
Relaxed system
Control with desired output (problem)
Fixed-point form
Relaxed system
Control on a sliding horizon (problem ): online and offline aspects
CPU time of the online control
Kleene star of the block tri-diagonal matrix and formal expressions of the sub-matrices
Conclusion
Bibliography
List of Symbols
Index
