Control of Linear Min-plus Systems under Temporal Constraints

Author

Amari, S. ; Demongodin, I. ; Loiseau, J.J.

Author_Institution

Institute of Research in Communications and Cybernetic of Nantes, 1 rue de la Noë BP 92101, 44321 Nantes cedex 03, France (phone: +33-240376978 ; e-mail: said.amari@irccyn.ec-nantes.fr).

fYear

2005

fDate

12-15 Dec. 2005

Firstpage

7738

Lastpage

7743

Abstract

We consider a class of controlled timed event graphs subject to strict temporal constraints. Such a graph is deterministic, in the sense that its behaviour only depends on the initial marking and on the control that is applied. This behaviour can be modelled by a system of difference equations that are linear in the Min-Plus algebra. The temporal constraint is represented by an inequality that is also linear in the min-plus algebra. Then, a method for the synthesis of a control law ensuring the respect of constraints is described. We give explicit formulas characterizing a control law, which, if two conditions are satisfied, ensures the validity of the temporal constraints. It is a causal state feedback, involving delays. The method is illustrated on an example.

Keywords

Algebra; Chemical industry; Control system synthesis; Control systems; Cybernetics; Delay; Difference equations; Food industry; State feedback; Time factors;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on

Print_ISBN

0-7803-9567-0

Type

conf

DOI

10.1109/CDC.2005.1583412

Filename

1583412