Recent Advances in Differential Equations and Control Theory
Recent Advances in Differential Equations and Control Theory

Author: Concepción Muriel

Publisher: Springer Nature

Published: 2021-03-13

Total Pages: 102

ISBN-13: 3030618757

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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.

Recent Advances in Differential Equations and Applications
Recent Advances in Differential Equations and Applications

Author: Juan Luis García Guirao

Publisher: Springer

Published: 2019-01-04

Total Pages: 250

ISBN-13: 3030003418

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This work gathers a selection of outstanding papers presented at the 25th Conference on Differential Equations and Applications / 15th Conference on Applied Mathematics, held in Cartagena, Spain, in June 2017. It supports further research into both ordinary and partial differential equations, numerical analysis, dynamical systems, control and optimization, trending topics in numerical linear algebra, and the applications of mathematics to industry. The book includes 14 peer-reviewed contributions and mainly addresses researchers interested in the applications of mathematics, especially in science and engineering. It will also greatly benefit PhD students in applied mathematics, engineering and physics.

Recent Advances in Differential Equations
Recent Advances in Differential Equations

Author: H-H Dai

Publisher: CRC Press

Published: 2020-01-30

Total Pages: 260

ISBN-13: 1000724549

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The First Pan-China Conference on Differential Equations was held in Kunming, China in June of 1997. Researchers from around the world attended-including representatives from the US, Canada, and the Netherlands-but the majority of the speakers hailed from China and Hong Kong. This volume contains the plenary lectures and invited talks presented at that conference, and provides an excellent view of the research on differential equations being carried out in China. Most of the subjects addressed arose from actual applications and cover ordinary and partial differential equations. Topics include:

Recent Advances in Differential Equations
Recent Advances in Differential Equations

Author: Roberto Conti

Publisher: Elsevier

Published: 2014-05-10

Total Pages: 462

ISBN-13: 1483273911

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Recent Advances in Differential Equations contains the proceedings of a meeting held at the International Center for Theoretical Physics in Trieste, Italy, on August 24-28, 1978 under the auspices of the U.S. Army Research Office. The papers review the status of research in the field of differential equations (ordinary, partial, and functional). Both theoretical aspects (differential operators, periodic solutions, stability and bifurcation, asymptotic behavior of solutions, etc.) and problems arising from applications (reaction-diffusion equations, control problems, heat flow, etc.) are discussed. Comprised of 33 chapters, this book first examines non-cooperative trajectories of n-person dynamical games and stable non-cooperative equilibria, followed by a discussion on the determination and application of Vekua resolvents. The reader is then introduced to generalized Hopf bifurcation; some Cauchy problems arising in computational methods; and boundary value problems for pairs of ordinary differential operators. Subsequent chapters focus on degenerate evolution equations and singular optimal control; stability of neutral functional differential equations; local exact controllability of nonlinear evolution equations; and turbulence and higher order bifurcations. This monograph will be of interest to students and practitioners in the field of mathematics.

Recent Advances in Differential Equations and its Applications (DEAPP–2017)
Recent Advances in Differential Equations and its Applications (DEAPP–2017)

Author: Dr. K.S. Lakshmi

Publisher: Allied Publishers

Published: 2017-08-10

Total Pages: 196

ISBN-13: 9385926780

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Differential Equations serve as mathematical models for virtually any natural or physical phenomena in science and technology and has applications even in diverse fields such as economics, medicine, ecology, etc. The seminar was organized to throw light on the recent advances in the applications of differential equations and to provide a platform for sharing the knowledge with experts in the field with young students and researchers. The Researchers and educators in the field of differential equations were invited to attend and share their rich experience. As for everything else. so for a mathematical theory. beauty can be perceived but not explained.

Trends in Control Theory and Partial Differential Equations
Trends in Control Theory and Partial Differential Equations

Author: Fatiha Alabau-Boussouira

Publisher: Springer

Published: 2019-07-04

Total Pages: 285

ISBN-13: 3030179494

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This book presents cutting-edge contributions in the areas of control theory and partial differential equations. Over the decades, control theory has had deep and fruitful interactions with the theory of partial differential equations (PDEs). Well-known examples are the study of the generalized solutions of Hamilton-Jacobi-Bellman equations arising in deterministic and stochastic optimal control and the development of modern analytical tools to study the controllability of infinite dimensional systems governed by PDEs. In the present volume, leading experts provide an up-to-date overview of the connections between these two vast fields of mathematics. Topics addressed include regularity of the value function associated to finite dimensional control systems, controllability and observability for PDEs, and asymptotic analysis of multiagent systems. The book will be of interest for both researchers and graduate students working in these areas.

Mathematical Control Theory
Mathematical Control Theory

Author: Eduardo D. Sontag

Publisher: Springer Science & Business Media

Published: 2013-11-21

Total Pages: 543

ISBN-13: 1461205778

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Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.

Differential Equations And Control Theory
Differential Equations And Control Theory

Author: Sergiu Aizicovici

Publisher: CRC Press

Published: 2001-10-02

Total Pages: 348

ISBN-13: 9780203902189

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Provides comprehensive coverage of the most recent developments in the theory of non-Archimedean pseudo-differential equations and its application to stochastics and mathematical physics--offering current methods of construction for stochastic processes in the field of p-adic numbers and related structures. Develops a new theory for parabolic equations over non-Archimedean fields in relation to Markov processes.

Optimal Control of Partial Differential Equations
Optimal Control of Partial Differential Equations

Author: Fredi Tröltzsch

Publisher: American Mathematical Society

Published: 2024-03-21

Total Pages: 417

ISBN-13: 1470476444

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Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization.

Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications
Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications

Author: El Hassan Zerrik

Publisher: Springer Nature

Published: 2019-08-26

Total Pages: 274

ISBN-13: 3030261492

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This book describes recent developments in a wide range of areas, including the modeling, analysis and control of dynamical systems, and explores related applications. The book provided a forum where researchers have shared their ideas, results on theory, and experiments in application problems. The current literature devoted to dynamical systems is quite large, and the authors’ choice for the considered topics was motivated by the following considerations. Firstly, the mathematical jargon for systems theory remains quite complex and the authors feel strongly that they have to maintain connections between the people of this research field. Secondly, dynamical systems cover a wider range of applications, including engineering, life sciences and environment. The authors consider that the book is an important contribution to the state of the art in the fuzzy and dynamical systems areas.