Hybrid dynamical systems theory and the Signal language

Author

Benveniste, Albert ; Le Guernic, Paul

Author_Institution

IRISA-INRIA, Rennes, France

Volume

35

Issue

5

fYear

1990

fDate

5/1/1990 12:00:00 AM

Firstpage

535

Lastpage

546

Abstract

The logic and synchronization characteristics of general dynamical systems called hybrid dynamical systems (HDS) are studied. The theory is related to discrete event dynamical system theory, but handles numerics as well as symbolics. It is supported by the programming language Signal and a mathematical model of general implicit dynamical systems. The core of the theory is the notion of HDS resolution which is based on a coding of any HDS into a dynamic graph which consists of a skew product of a polynomial dynamical system on the finite field of integers modulo 3 (to describe the transitions of the underlying automation) and directed graphs (to describe how data dependencies dynamically evolve). The resolution algorithms are based on the study of this dynamical system

Keywords

automata theory; control system analysis computing; directed graphs; discrete time systems; encoding; formal logic; synchronisation; Signal; coding; directed graphs; discrete event dynamical system; dynamic graph; hybrid dynamical systems; integers modulo 3; logic; numerics; programming language; symbolics; synchronization; Aerospace electronics; Automatic control; Control systems; Dynamic programming; Logic programming; Mathematical programming; Real time systems; Robotics and automation; Signal processing algorithms; Signal resolution;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.53519

Filename

53519