Partial Differential Equations and Group T...

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Beschreibung

Ordinary differential control thPory (the classical theory) studies input/output re lations defined by systems of ordinary differential equations (ODE). The various con cepts that can be introduced (controllability, observability, invertibility, etc. ) must be tested on formal objects (matrices, vector fields, etc. ) by means of formal operations (multiplication, bracket, rank, etc. ), but without appealing to the explicit integration (search for trajectories, etc. ) of the given ODE. Many partial results have been re cently unified by means of new formal methods coming from differential geometry and differential algebra. However, certain problems (invariance, equivalence, linearization, etc. ) naturally lead to systems of partial differential equations (PDE). More generally, partial differential control theory studies input/output relations defined by systems of PDE (mechanics, thermodynamics, hydrodynamics, plasma physics, robotics, etc. ). One of the aims of this book is to extend the preceding con cepts to this new situation, where, of course, functional analysis and/or a dynamical system approach cannot be used. A link will be exhibited between this domain of applied mathematics and the famous 'Backlund problem', existing in the study of solitary waves or solitons. In particular, we shall show how the methods of differ ential elimination presented here will allow us to determine compatibility conditions on input and/or output as a better understanding of the foundations of control the ory. At the same time we shall unify differential geometry and differential algebra in a new framework, called differential algebraic geometry.

Inhaltsverzeichnis

I. Homological Algebra.- II. Jet Theory.- III. Nonlinear Systems.- IV. Linear Systems.- V. Group Theory.- VI. Differential Galois Theory.- VII. Control Theory.- VIII. Continuum Physics.

Details

Erscheinungsjahr:	1994
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	x 478 S.
ISBN-13:	9780792329664
ISBN-10:	079232966X
Sprache:	Englisch
Herstellernummer:	11248552
Einband:	Gebunden
Autor:	Pommaret, J. F.
Hersteller:	Springer Netherland Springer Netherlands
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 31 mm
Von/Mit:	J. F. Pommaret
Erscheinungsdatum:	30.06.1994
Gewicht:	0,898 kg

Artikel-ID: 102455638

Inhaltsverzeichnis

I. Homological Algebra.- II. Jet Theory.- III. Nonlinear Systems.- IV. Linear Systems.- V. Group Theory.- VI. Differential Galois Theory.- VII. Control Theory.- VIII. Continuum Physics.

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