Algebraic and symbolic computation methods in dynamical systems

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

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...

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Bibliographic Details
Other Authors: Quadrat, Alban, Zerz, Eva
Format: eBook
Language:English
Published: Cham : Springer, 2020.
Series:Advances in delays and dynamics ; v. 9.
Subjects:
Differential-algebraic equations.
Dynamics & vibration.
Calculus of variations.
Cybernetics & systems theory.
Technology & Engineering > Mechanical.
Mathematics > Calculus.
Science > System Theory.
Cálculo de variaciones
Matemáticas > Cálculo
Differential-algebraic equations
Electronic books.
Online Access:Click for online access
Table of Contents:
  • 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 Modules
  • 2.4 Characterization of Isomorphic Modules
  • 2.5 The Unimodular Completion Problem
  • References
  • 3 Computing Polynomial Solutions and Annihilators of Integro-Differential Operators with Polynomial Coefficients
  • 3.1 Introduction
  • 3.2 The Ring of Ordinary Integro-Differential Operators with Polynomial Coefficients
  • 3.3 Normal Forms
  • 3.4 Several Evaluations
  • 3.5 Syzygies and Annihilators
  • 3.6 Fredholm and Finite-Rank Operators
  • 3.7 Polynomial Solutions of Rational Indicial Maps and Polynomial Index
  • 3.8 Polynomial Solutions and Annihilators
  • References
  • Part II Symbolic Methods for Nonlinear Dynamical Systems and for Applications to Observation and Estimation Problems
  • 4 Thomas Decomposition and Nonlinear Control Systems
  • 4.1 Introduction
  • 4.2 Thomas Decomposition
  • 4.2.1 Algebraic Systems
  • 4.2.2 Differential Systems
  • 4.3 Elimination
  • 4.4 Control-Theoretic Applications
  • 4.5 Conclusion
  • References
  • 5 Some Control Observation Problems and Their Differential Algebraic Partial Solutions
  • 5.1 Introduction
  • 5.2 The Differential Algebraic Approach
  • 5.3 How Does It Compare to the Classical Theory?
  • 5.4 Partial Answers to Some Observation Problems
  • 5.4.1 Computing
  • 5.5 Regular Observability
  • 5.5.1 Sensor Selection
  • 5.6 Some of the Questions Without Partial Answers
  • 5.6.1 A Foundation Problem
  • 5.6.2 Robustness
  • 5.6.3 Decision Methods Problems
  • References
  • 6 On Symbolic Approaches to Integro-Differential Equations
  • 6.1 Introduction
  • 6.2 Origin of Integro-Differential Models
  • 6.2.1 Hereditary Theories
  • 6.2.2 Some Classical Integro-Differential Models
  • 6.3 Integro-Differential Equations for Parameter Estimation

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