Discrete event systems in dioid algebra and conventional algebra / Philippe Declerck.

Format:

Book

Author/Creator:

Clerck, Philippe de.

Series:

Focus series (London, England)

Focus series in automation & control, 2051-2481

Language:

English

Subjects (All):

Algebra.

Discrete-time systems.

Physical Description:

1 online resource (166 p.)

Edition:

1st ed.

Place of Publication:

London : ISTE, 2013.

Language Note:

English

Summary:

This book concerns the use of dioid algebra as (max, +) algebra to treat the synchronization of tasks expressed by the maximum of the ends of the tasks conditioning the beginning of another task - a criterion of linear programming. A classical example is the departure time of a train which should wait for the arrival of other trains in order to allow for the changeover of passengers.The content focuses on the modeling of a class of dynamic systems usually called "discrete event systems" where the timing of the events is crucial. Events are viewed as sudden changes in a process which i

Contents:

Title Page; Contents; Chapter 1. Introduction; 1.1. General introduction; 1.2. History and three mainstays; 1.3. Scientific context; 1.3.1. Dioids; 1.3.2. Petri nets; 1.3.3. Time and algebraic models; 1.4. Organization of the book; Chapter 2. Consistency; 2.1. Introduction; 2.1.1. Models; 2.1.2. Physical point of view; 2.1.3. Objectives; 2.2. Preliminaries; 2.3. Models and principle of the approach; 2.3.1. P-time event graphs; 2.3.2. Dater form; 2.3.3. Principle of the approach (example 2); 2.4. Analysis in the "static" case; 2.5. "Dynamic" model

3.2.6. Existence of a 1-periodic behavior3.2.7. Example continued; 3.3. Optimization; 3.3.1. Approach 1; 3.3.2. Example continued; 3.3.3. Approach 2; 3.4. Conclusion; 3.5. Appendix; Chapter 4. Control with Specifications; 4.1. Introduction; 4.2. Time interval systems; 4.2.1. (min, max, +) algebraic models; 4.2.2. Timed event graphs; 4.2.3. P-time event graphs; 4.2.4. Time stream event graphs; 4.3. Control synthesis; 4.3.1. Problem; 4.3.2. Pedagogical example: education system; 4.3.3. Algebraic models; 4.4. Fixed-point approach; 4.4.1. Fixed-point formulation; 4.4.2. Existence

4.4.3. Structure4.5. Algorithm; 4.6. Example; 4.6.1. Models; 4.6.2. Fixed-point formulation; 4.6.3. Existence; 4.6.4. Optimal control with specifications; 4.6.5. Initial conditions; 4.7. Conclusion; Chapter 5. Online Aspect of Predictive Control; 5.1. Introduction; 5.1.1. Problem; 5.1.2. Specific characteristics; 5.2. Control without desired output (problem 1); 5.2.1. Objective; 5.2.2. Example 1; 5.2.3. Trajectory description; 5.2.4. Relaxed system; 5.3. Control with desired output (problem 2); 5.3.1. Objective; 5.3.2. Fixed-point form; 5.3.3. Relaxed system

5.4. Control on a sliding horizon (problem 3): online and offline aspects5.4.1. CPU time of the online control; 5.5. Kleene star of the block tri-diagonal matrix and formal expressions of the sub-matrices; 5.6. Conclusion; Bibliography; List of Symbols; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-118-57968-2

1-299-24211-1

1-118-57965-8

OCLC:

829460542