Algebraic and symbolic computation methods in dynamical systems

by Quadrat, Alban Zerz, Eva

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Title Statements

Full title :Algebraic and symbolic computation methods in dynamical systems / Alban Quadrat, Eva Zerz, editors.

Summary

This book aims at reviewing recent progress in the direction of algebraic and symbolic computation methods for functional systems, e.g. ODE systems, differential time-delay equations, difference equations and integro-differential equations. In the nineties, modern algebraic theories were introduced in mathematical systems theory and in control theory. Combined with real algebraic geometry, which was previously introduced in control theory, the past years have seen a flourishing development of algebraic methods in control theory. One of the strengths of algebraic methods lies in their close connections to computations. The use of the above-mentioned algebraic theories in control theory has been an important source of motivation to develop effective versions of these theories (when possible). With the development of computer algebra and computer algebra systems, symbolic methods for control theory have been developed over the past years. The goal of this book is to propose a partial state of the art in this direction. To make recent results more easily accessible to a large audience, the chapters include materials which survey the main mathematical methods and results and which are illustrated with explicit examples.

Edition Statements

Publication Date:2020.

Publication Statements

Publisher(s):Springer
Place of Publication:Cham
Language:eng
Publication Date:2020.

Notes

6.3.1 Statement of the Estimation Problem

The Physical Object

Description:1 online resource (320 pages)

Edition Identifiers

ISBN:9783030383565, 3030383563
oclc:on1157096320
LC Classification:QA372.5
Dewey Decimal:512/.56

Intro -- Preface -- Part I. Effective Algebraic Methods for Linear Functional Systems -- Part II. Symbolic Methods for Nonlinear Dynamical Systems and for Applications to Observation and Estimation Problems -- Part III. Algebraic Geometry Methods for Systems and Control Theory -- Contents -- Part I Effective Algebraic Methods for Linear Functional Systems -- 1 Effective Algebraic Analysis Approach to Linear Systems over Ore Algebras -- 1.1 Introduction -- 1.2 Linear Systems over Ore Algebras -- 1.3 Gröbner Basis Techniques -- 1.3.1 Gröbner Bases for Ideals over Ore Algebras

1.3.2 Gröbner Bases for Modules over Ore Algebras -- 1.4 Algebraic Analysis Approach to Linear Systems Theory -- 1.4.1 Linear Functional Systems and Finitely Presented Left Modules -- 1.4.2 Basic Results of Homological Algebra -- 1.4.3 Dictionary Between System Properties and Module Properties -- 1.5 Mathematica Packages -- 1.5.1 The HolonomicFunctions Package -- 1.5.2 The OreAlgebraicAnalysis Package -- References -- 2 Equivalences of Linear Functional Systems -- 2.1 Introduction -- 2.2 Linear Functional Systems and Finitely Presented Left Modules

2.3 Homomorphisms of Behaviors/Finitely Presented Left Module…

Subjects

Calculus of variations Cybernetics & systems theory Differential-algebraic equations Dynamics & vibration Équations différentielles algébriques MATHEMATICS -- Calculus Science -- System Theory TECHNOLOGY & ENGINEERING -- Mechanical