Recent Advances in Differential Equations and Control Theory

✍ Scribed by Concepción Muriel, Carmen Pérez-Martinez

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 109
• Series: SEMA SIMAI Springer Series, 9
• Category: Library

✦ Synopsis

This book collects the latest results and new trends in the application of mathematics to some problems in control theory, numerical simulation and differential equations.  The work comprises the main results presented at a thematic minisymposium, part of the 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), held in Valencia, Spain, from 15 to 18 July 2019. The topics covered in the 6 peer-review contributions involve applications of numerical methods to real problems in oceanography and naval engineering, as well as relevant results on switching control techniques, which can have multiple applications in industrial complexes, electromechanical machines, biological systems, etc. Problems in control theory, as in most engineering problems, are modeled by differential equations, for which standard solving procedures may be insufficient. The book also includes recent geometric and analytical methods for the search of exact solutions for differential equations, which serve as essential tools for analyzing problems in many scientific disciplines.

✦ Table of Contents

Preface
Contents
Editors and Contributors
About the Editors
Contributors
The Upwelling of the Colombian Caribbean Coasts: Remote Sensing, Morphology, and Influence on the Lake Maracaibo
1 Introduction
2 Materials and Methods
2.1 Satellite Imagery, Area Under Study, and Data Sets
2.2 Mathematical Morphology and Fractal Dimension
2.3 Numerical Model
3 Results
3.1 Wind Study in the Area
3.2 The Upwelling of La Guajira
3.3 Outflow of Lake Maracaibo
4 Conclusions
References
Is it possible to use Discontinuous Shapes in Hydrodynamics?
1 Introduction
2 The NACA and KNACA Profiles
3 Results
4 Conclusions
References
Stabilization of Third Order Switched Linear Systems via InvariantSet
1 Introduction
2 Preliminaries
3 Sufficient Condition for Stabilization
4 Example
5 Conclusions
References
Control of Second-Order Switched Systems with Application to DC–DC Converters
1 Introduction
2 Preliminaries
3 Switched Transference of Second-Order Switched Systems
4 Application to DC–DC Converter Models
4.1 Buck Converter
4.2 Boost Converter
5 Conclusions
References
Symbolic Computation Algorithms for Second-Order ODEs by Using Two λ-Symmetries
1 Definitions and Main Results Concerning the Algorithms
1.1 Generalized Commuting Symmetries from Two Known λ-Symmetries
1.2 Integrating Factors, First Integrals, and Jacobi Last Multipliers
1.3 Integrating Factors of the Reduced and Auxiliary Equations
2 The Procedure TwoLambdaSym
2.1 Description
3 Examples of the Usage of the Procedure TwoLambdaSym
3.1 Example 1
3.2 Example 2
3.3 Example 3
4 Concluding Remark
Appendix: The Maple Procedure TwoLambdaSym
References
Systems of Vector Fields for the Integration of Ordinary Differential Equations
1 Introduction
2 Preliminaries
2.1 Lie Point Symmetries
2.2 λ-Symmetries
2.3 Solvable Structures
3 Systems of Vector Fields for Second-Order ODEs
3.1 Case 1: Using a Known Lie Point Symmetry
3.2 Case 2: Using a Known λ-Symmetry
3.2.1 Application to Liénard I-Type Equations
4 Systems of Vector Fields for SL(2,R)-Invariant Third-Order ODEs
5 Generalised Solvable Structures for nth-Order ODEs
6 Conclusions
References