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