Hybrid dynamical systems theory and nonlinear dynamical systems over finite fields

Author

Benveniste, Albert ; Le Guernic, Paul

Author_Institution

INRIA, Rennes, France

fYear

1988

fDate

7-9 Dec 1988

Firstpage

209

Abstract

The authors study the logic and synchronization characteristics of general dynamical systems called hybrid dynamical systems (HDSs). The proposed theory generalizes the notion of discrete-event dynamical systems by handling numerics as well as symbolics. This theory is supported by the programming language SIGNAL and a mathematical model of relational style. This framework makes it possible to formulate in the same way HDS programming or specification and HDS control. The core of the theory is the notion of HDS resolution, which is based on a reduction technique that maps any HDS specification program into a polynomial dynamical system on the finite field of integers modulo 3; all the algorithms are then based on the study of this dynamical system

Keywords

concurrency control; discrete systems; nonlinear systems; specification languages; concurrency control; discrete event systems; dynamical systems theory; finite fields; hybrid systems; logic; modulo 3; nonlinear systems; numerics; polynomial system; programming language SIGNAL; reduction technique; resolution; specification languages; symbolics; synchronization; Control systems; Dynamic programming; Galois fields; Logic programming; Mathematical model; Mathematical programming; Nonlinear dynamical systems; Polynomials; Signal processing; Signal resolution;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1988., Proceedings of the 27th IEEE Conference on

Conference_Location

Austin, TX

Type

conf

DOI

10.1109/CDC.1988.194297

Filename

194297