Matematik for ingeniører

This book offers a thorough introduction to the basics and scientific and technological innovations involved in the modern study of reinforcement-learning-based feedback control. The authors address a wide variety of systems including work on nonlinear, networked, multi-agent and multi-player systems. A concise description of classical reinforcement learning (RL), the basics of optimal control with dynamic programming and network control architectures, and a brief introduction to typical algorithms build the foundation for the remainder of the book. Extensive research on data-driven robust control for nonlinear systems with unknown dynamics and multi-player systems follows. Data-driven optimal control of networked single- and multi-player systems leads readers into the development of novel RL algorithms with increased learning efficiency. The book concludes with a treatment of how these RL algorithms can achieve optimal synchronization policies for multi-agentsystems with unknown model parameters and how game RL can solve problems of optimal operation in various process industries. Illustrative numerical examples and complex process control applications emphasize the realistic usefulness of the algorithms discussed. The combination of practical algorithms, theoretical analysis and comprehensive examples presented in Reinforcement Learning will interest researchers and practitioners studying or using optimal and adaptive control, machine learning, artificial intelligence, and operations research, whether advancing the theory or applying it in mineral-process, chemical-process, power-supply or other industries.

Dynamics of Civil Structures, Volume 2:  Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022, the second volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of the Dynamics of Civil Structures, including papers on:Structural VibrationHumans & StructuresInnovative Measurement for Structural ApplicationsSmart Structures and Automation Modal Identification of Structural SystemsBridges and Novel Vibration AnalysisSensors and Control 

Advanced manufacturing via computer numerical machining is the art of producing mechanical components employed in aerospace, automobile, and industrial applications where a high level of accuracy is needed. This book focuses on the nano-machining of aluminum alloy and its optimization. The application of aluminum alloy in the manufacturing industry has increased tremendously due to its lightweight to high strength ratio and high-level resistance to corrosion. However, aluminum alloy has some challenges during the machining and manufacturing stage in order to solve real-life manufacturing challenges in advanced machining operation for sustainable production processes. Therefore, it is a need for the implementation of a general algebraic modeling system (GAMS) and other metaheuristic techniques for problem solving and to effectively develop mathematical models for high accuracy prediction and optimization under nano-lubrication machining conditions. This book discusses majorly on themajor three responses in machining such as surface roughness, cutting force, and material removal rate, which will give an excellent guide to undergraduate and postgraduate students, senior research fellows in academia, operational, and strategic staff in manufacturing industries.

This primer on averaging theorems provides a practical toolbox for applied mathematicians, physicists, and engineers seeking to apply the well-known mathematical theory to real-world problems. With a focus on practical applications, the book introduces new approaches to dissipative and Hamiltonian resonances and approximations on timescales longer than 1/¿.Accessible and clearly written, the book includes numerous examples ranging from elementary to complex, making it an excellent basic reference for anyone interested in the subject. The prerequisites have been kept to a minimum, requiring only a working knowledge of calculus and ordinary and partial differential equations (ODEs and PDEs).In addition to serving as a valuable reference for practitioners, the book could also be used as a reading guide for a mathematics seminar on averaging methods. Whether you're an engineer, scientist, or mathematician, this book offers a wealth of practicaltools and theoretical insights to help you tackle a range of mathematical problems.

This book focuses on selected methods of applied mathematics that are aimed at mathematical optimization, with an emphasis on their application in engineering practice. It delves into the current mathematical modeling of processes and systems, with a specific focus on the optimization modeling of technological processes. The authors discuss suitable linear, convex, and nonlinear optimization methods for solving problems in engineering practice. Real-world examples and data are used to numerically illustrate the implementation of these methods, utilizing the popular MATLAB software system and its extension to convex optimization. The book covers a wide range of topics, including mathematical modeling, linear programming, convex programming, and nonlinear programming, all with an engineering optimization perspective. It serves as a comprehensive guide for engineers, researchers, and students interested in the practical application of optimization methods in engineering.

The International Scientific and Technical Conference ¿Integrated Computer Technologies in Mechanical Engineering¿¿Synergetic Engineering (ICTM) was established by National Aerospace University ¿Kharkiv Aviation Institute.¿ The Conference ICTM¿2022 was held in Kharkiv, Ukraine, during November 18¿20, 2022. During this conference, technical exchanges between the research community were carried out in the forms of keynote speeches, panel discussions, as well as special session. In addition, participants were treated to a series of receptions, which forge collaborations among fellow researchers. ICTM¿2022 received 137 papers submissions from different countries. All of these offer us plenty of valuable information and would be of great benefit to experience exchange among scientists in modeling and simulation. The organizers of ICTM¿2022 made great efforts to ensure the success of this conference. We hereby would like to thank allthe members of ICTM¿2022 Advisory Committee for their guidance and advice, the members of program committee and organizing committee, and the referees for their effort in reviewing and soliciting the papers, and all authors for their contribution to the formation of a common intellectual environment for solving relevant scientific problems. Also, we grateful to Springer¿Janusz Kacprzyk and Thomas Ditzinger as the editor responsible for the series ¿Lecture Notes in Networks and Systems¿ for their great support in publishing these selected papers.

This monograph contains an in-depth and coherent treatment of dimension-reduced modeling of blood flows on the level of large vessels (macrocirculation). The authors reduce the complexity by combining a one-dimensional Navier-Stokes equation and a simplified FSI-concept. The influence of omitted vessels, which are subsequent to the outlets of larger vessels, is accounted for by systems of ordinary differential equations (0D models). The target audience primarily comprises research experts in the field of biomedical engineering, but the book may also be beneficial for graduate students alike.

This book collects the results presented at the 158th European Study Group with Industry, which took place at the Centre de Recerca Matemàtica in Barcelona in January 2020. The European Study Groups with Industry are a well-recognised forum where mathematicians work with industrial representatives on issues of current interest to companies. At this particular meeting, the problems were chosen to provide a wide variety of subject areas and to appeal to local academics. In this work, the research carried out and the solutions presented to the companies are detailed. In particular, the book focuses on: estimating the difficulty level of mobile games; modelling the stability of human towers; fibre coating in the manufacture of clutch components; safe trajectories of robot arms. The book provides an excellent addition to the canon of Industrial Mathematics. It is addressed to researchers keen to apply mathematics to topical, real-world problems.

This book introduces and provides a detailed understanding of on- and off-road vehicle dynamics. It discusses classical on-road tyre mechanics, including finite element tyre modelling and validation, using a combination of theoretical and experimental data sets. Chapters explore new computational techniques that describe terrain models and combined to develop better off-road vehicle models, and focus is placed on terrain characterization and modelling, using two popular modelling techniques, as well as performance characteristics of off-road vehicles - including rolling and driven combinations, traction, and steering. The effect of multi-pass and soil compaction on tyre performance is described as well.The book presents a unique neuro-tyre model for both on-road and off-road situations, capable of computing the steering, braking characteristics, and soil compaction. Road vehicle characteristics are described, including the stability and control, roll centre and roll axis, androllover mechanics. The road vehicle braking performance is also described, including the brake components, choice of brake, and the transient load transfer. Finally, the dynamics and control of multi-wheel combat vehicles are presented and described extensively.The book is dedicated to undergraduate and graduate engineering students, in addition to researchers, and the automotive industry. As well as provide the readers with a better understanding of vehicle dynamics and soil mechanics. The book is also beneficial for automotive industries looking for a quick and reliable model to be implemented in their main software.

Networked switched system has emerged as an essential system model in the field of control due to its accurate reflection of the wide-area distribution and typical switching characteristics of increasingly sophisticated controlled objects in engineering practice. The openness of communication networks, the limitation of communication resources, and the complexity of switching behaviors make it a challenging task to ensure the steady-state and transient performance of the output regulation of networked switched systems. This book proposes several novel methodologies for output regulation of networked switched systems from the perspective of both steady-state and transient performance. The core features of our approaches are fourfold: i) Without imposing stability requirements on individual subsystems and all switching instants, a series of innovative dwell-time switching technologies are established to handle the issue of output regulation for networked switched systems with severely unstable dynamics under event-triggering strategies in the presence of cyber attacks. ii) Taking into account switching rules and cyber attack parameters within the event-triggered control framework, event detection conditions, modal matching conditions, and event waiting conditions are constructed, and a series of new event-triggering mechanisms are proposed to effectively enhance network resource utilization and secure steady-state performance of networked switched systems. iii) Typical cyber attacks have unique consequences on the secure steady-state performance of networked switched systems with severely unstable dynamics due to the short activation time of a single subsystem and the necessity to relay the switching signal through the network. To this purpose, the consecutive asynchronous switching behaviors of the subsystem or controller resulting from a long-duration DoS attack or an integrity deception attack incorporating switching signal tampering are investigated. iv) To deal with the transient performance fluctuations of the closed-loop system caused by factors such as mismatch switching between the subsystem and the corresponding controller, data update at event-triggering instants, cyber attack blocking and tampering of transmitted data, etc., bumpless transfer control strategies are formulated in the interpolation type and multi-source type, balancing the transient and steady-state performances of the output regulation of networked switched systems. This book presents these topics in a systematic way, which is of tremendous importance to both theoretical research and practical applications involving switched systems.

This book presents a new search paradigm for solving the Traveling Salesman Problem (TSP). The intrinsic difficulty of the TSP is associated with the combinatorial explosion of potential solutions in the solution space. The author introduces the idea of using the attractor concept in dynamical systems theory to reduce the search space for exhaustive search for the TSP. Numerous examples are used to describe how to use this new search algorithm to solve the TSP and its variants including: multi-objective TSP, dynamic TSP, and probabilistic TSP. This book is intended for readers in the field of optimization research and application.

This book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, efficient software implementations, and interesting practical case studies. This is the first book presenting to the readers interested in optimization the advantages of a recently introduced supercomputing paradigm that allows to numerically work with different infinities and infinitesimals on the Infinity Computer patented in several countries. One of the editors of the book is the creator of the Infinity Computer, and another editor was the first who has started to use it in optimization. Their results were awarded by numerous scientific prizes. This engaging book opens new horizons for researchers, engineers, professors, and students with interests in supercomputing paradigms, optimization, decision making, game theory, and foundations of mathematics and computer science."e;Mathematicians have never been comfortable handling infinities... But an entirely new type of mathematics looks set to by-pass the problem... Today, Yaroslav Sergeyev, a mathematician at the University of Calabria in Italy solves this problem... "e;MIT Technology Review"e;These ideas and future hardware prototypes may be productive in all fields of science where infinite and infinitesimal numbers (derivatives, integrals, series, fractals) are used."e; A. Adamatzky, Editor-in-Chief of the International Journal of Unconventional Computing."e;I am sure that the new approach ... will have a very deep impact both on Mathematics and Computer Science."e; D. Trigiante, Computational Management Science."e;Within the grossone framework, it becomes feasible to deal computationally with infinite quantities, in a way that is both new (in the sense that previously intractable problems become amenable to computation) and natural"e;. R. Gangle, G. Caterina, F. Tohme, Soft Computing."e;The computational features offered by the Infinity Computer allow us to dynamically change the accuracy of representation and floating-point operations during the flow of a computation. When suitably implemented, this possibility turns out to be particularly advantageous when solving ill-conditioned problems. In fact, compared with a standard multi-precision arithmetic, here the accuracy is improved only when needed, thus not affecting that much the overall computational effort."e; P. Amodio, L. Brugnano, F. Iavernaro & F. Mazzia, Soft Computing

Dieses Lehrbuch entwickelt die Konzepte und Werkzeuge der linearen Algebra zusammen mit anspruchsvollen und praxisrelevanten Anwendungen aus dem Ingenieurswesen. Dabei stellt es die Theorie soweit exakt dar, dass eine tragfähige Grundlage für die späteren Entwicklungen entsteht ¿ die Umsetzung mit dem Computer wird aber ebenfalls explizit erläutert. Das Buch macht somit letztlich weiterführende Konzepte und ihre Anwendungen mit der gleichen geometrischen Intuition zugänglich, wie es bei elementaren Konzepten im ersten Semester üblich ist. Der gaußsche Eliminationsalgorithmus etwa löst nicht nur Gleichungssysteme ¿ wenn man die Darstellung als Tableau genügend weit entwickelt, kann man damit auch inverse Matrizen berechnen, die Lösungsmenge ablesen, feststellen, ob zwei Polynome einen gemeinsamen Teiler haben und jedes beliebige lineare Schnittproblem der Vektorgeometrie auf eine einheitliche Art mit einem einzigen Tableau lösen. Mit Matrizen kann man nicht nur Gleichungssysteme aufstellen und lösen, man kann damit auch optische Systeme modellieren, den größten gemeinsamen Teiler finden, unabhängige Zyklen für die Kirchhoff-Gleichungen berechnen oder mit Drehmatrizen die Quadraturamplitudenmodulation als Grundlage von Software Defined Radio verstehen.

Model Validation and Uncertainty Quantification, Volume 3:  Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics, 2021, the third volume of nine from the Conference brings together contributions to this important area of research and engineering.  The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on:Inverse Problems and Uncertainty QuantificationControlling UncertaintyValidation of Models for Operating EnvironmentsModel Validation & Uncertainty Quantification: Decision MakingUncertainty Quantification in Structural DynamicsUncertainty in Early Stage DesignComputational and Uncertainty Quantification Tools

This volume highlights the latest advances, innovations, and applications in the field of sustainable concrete structures, as presented by scientists and engineers at the RILEM International Conference on Numerical Modeling Strategies for Sustainable Concrete Structures (SSCS), held in Marseille, France, on July 4-6, 2022. It demonstrates that numerical methods (finite elements, finite volumes, finite differences) are a relevant response to the challenge to optimize the utilization of cement in concrete constructions while checking that these constructions have a lifespan compatible with the stakes of sustainable development. They are indeed accurate tools for an optimized design of concrete constructions, and allow us to consider all types of complexities: for example, those linked to rheological, physicochemical and mechanical properties of concrete, those linked to the geometry of the structures or even to the environmental boundary conditions. This optimization must also respect constraints of time, money, security, energy, CO2 emissions, and, more generally, life cycle more reliably than the codes and analytical approaches currently used. Numerical methods are, undoubtedly, the best calculation tools at the service of concrete eco-construction. The contributions present traditional and new ideas that will open novel research directions and foster multidisciplinary collaboration between different specialists.

The NUMISHEET conference series is the most significant international conference on the area of the numerical simulation of sheet metal forming processes. It gathers the most prominent experts in numerical methods in sheet forming processes and is an outstanding forum for the exchange of ideas and for the discussion of technologies related to sheet metal forming processes. Topics covered in this volume include but are not limited to the following: Materials Modeling and Experimental Testing MethodsFriction and ContactFormability, Necking, and FractureInstabilities and Surface DefectsFracture and DamageNumerical MethodsSpringbackIncremental Sheet FormingRoll FormingInnovative Forming MethodsProduct and Process Design and Optimization

This book highlights an analytical solution for the dynamics of axially rotating objects. It also presents the theory of gyroscopic effects, explaining their physics and using mathematical models of Euler's form for the motion of movable spinning objects to demonstrate these effects. The major themes and approaches are represented by the spinning disc and the action of the system of interrelated inertial torques generated by the centrifugal and Coriolis forces, as well as the change in the angular momentum. The interrelation of inertial torques is based on the dependency of the angular velocities of the motions of the spinning objects around axes by the principle of mechanical energy conservation. These kinetically interrelated torques constitute the fundamental principles of the mechanical gyroscope theory that can be used for any rotating objects of different designs, like rings, cones, spheres, paraboloids, propellers, etc. Lastly, the mathematical models for the gyroscopic effects are validated by practical tests.  The 2nd edition became necessary due to new development and corrections of mathematical expressions: It contains new chapters about the Tippe top inversion and inversion of the spinning object in an orbital flight and the boomerang aerodynamics.

This edited book considers social systems as self-organizing structures that reproduce new structural elements endowed with certain functional connections. The authors analyze innovative processes in social systems, leading to the sustainable convergence of knowledge and the emergence of technologies that improve the level of material well-being in society. The book summarizes research results in the field of digitalization and reveals deep connections with social problems. In addition, the book presents a whole array of innovative research on social systems management and the application of knowledge and intelligence to the solution of social problems. The contributing scholars and practitioners reflect on various types of social systems and assess the influence of disruptive factors from natural and coupled human-natural environments, discussing possible mechanisms for their neutralization.Sustainable development of social systems is among the most important tasks facingthe contemporary world. The contributed book highlights challenges to the sustainability of social systems, draws sociotechnical images of the future world order generated by the rapid development of intellectual technologies, and critically analyzes promising concepts for more sustainable social future. Among the discussed topics in the book are social governance, digital economy, technological landscapes, social systems modeling and simulation, cyber-social systems, knowledge-based innovation systems, complex processes in social systems, institutional arrangements, and other advancing research areas.The high-quality and original studies presented in the book appeal to those interested in broadening their perspectives on complexity science, complex social systems research, complex systems management, advanced technological development in social systems, etc. Since the book is rich with well-thought theories, advanced research approaches, and interdisciplinary research results, it becomes a great source of new ideas and insights on complex social systems.

This textbook focuses on the basics and complex themes of group theory taught to senior undergraduate mathematics students across universities. The contents focus on the properties of groups, subgroups, cyclic groups, permutation groups, cosets and Lagrange¿s theorem, normal subgroups and factor groups, group homomorphisms and isomorphisms, automorphisms, direct products, group actions and Sylow theorems. Pedagogical elements such as end of chapter exercises and solved problems are included to help understand abstract notions. Intermediate lemmas are also carefully designed so that they not only serve the theorems but are also valuable independently. The book is a useful reference to undergraduate and graduate students besides academics.

This book acts as a guide to simple models that describe some of the complex fluid dynamics, heat/mass transfer and combustion processes in droplets and sprays. Attention is focused mainly on the use of classical hydrodynamics, and a combination of kinetic and hydrodynamic models, to analyse the heating and evaporation of mono- and multi-component droplets. The models were developed for cases when small and large numbers of components are present in droplets. Some of these models are used for the prediction of time to puffing/micro-explosion of composite water/fuel droplets - processes that are widely used in combustion devices to stimulate disintegration of relatively large droplets into smaller ones. The predictions of numerical codes based on these models are validated against experimental results where possible. In most of the models, droplets are assumed to be spherical; some preliminary results of the generalisation of these models to the case of non-spherical droplets, approximating them as spheroids, are presented.

This book involves ideas/results from the topics of mathematical, information, and data sciences, in connection with the main research interests of Professor Pardo that can be summarized as Information Theory with Applications to Statistical Inference. This book is a tribute to Professor Leandro Pardo, who has chaired the Department of Statistics and OR of the Complutense University in Madrid, and he has been also President of the Spanish Society of Statistics and Operations Research.  In this way, the contributions have been structured into three parts, which often overlap to a greater or lesser extent, namely Trends in Mathematical Sciences (Part I) Trends in Information Sciences (Part II) Trends in Data Sciences (Part III) The contributions gathered in this book have offered either new developments from a theoretical and/or computational and/or applied point of view, or reviews of recent literature of outstanding developments. They have been applied through nice examples in climatology, chemistry, economics, engineering, geology, health sciences, physics, pandemics, and socioeconomic indicators. Consequently, the intended audience of this book is mainly statisticians, mathematicians, computer scientists, and so on, but users of these disciplines as well as experts in the involved applications may certainly find this book a very interesting read.

Automatic Control with Interactive Tools is a textbook for undergraduate study of automatic control. Providing a clear course structure, and covering concepts taught in engineering degrees, this book is an ideal companion to those studying or teaching automatic control. The authors have used this text successfully to teach their students.By providing unique interactive tools, which have been designed to illustrate the most important automatic control concepts, Automatic Control with Interactive Tools helps students overcome the potential barriers presented by the significant mathematical content of automatic control courses. Even when they have previously had only the benefit of an introductory control course, the software tools presented will help readers to get to grips with the use of such techniques as differential equations, linear algebra, and differential geometry. This textbook covers the breadth of automatic control topics, including time responses of dynamic systems, the Nyquist criterion and PID control. It switches smoothly between analytical and practical approaches. Automatic Control with Interactive Tools offers a clear introduction to automatic control, ideal for undergraduate students, instructors and anyone wishing to familiarize themselves with the fundamentals of the subject

This textbook is intended to display a broad, methodological introduction to geoinformatics and geoinformation science. It deals with the recording, modeling, processing and analysis as well as presenting and distributing of geodata. As an integrated approach it is dedicated to the multidisciplinary application of methods and concepts of computer science to solve spatial tasks. First the reader receives an introduction to the approach and tasks of geoinformatics, basic concepts and general principles of information processing as well as essentials of computer science. Then this textbook focuses on the following topics: spatial reference systems, digital spatial data, interoperability of spatial data, visualization of spatial information, data organization and database systems, geoinformation systems, remote sensing and digital image processing.The result is a comprehensive manual for studies and practical applications in geoinformatics. It serves also as a basis to support and deepen methodological courses in geography, geology, geodesy and surveying as well as all environmental sciences. In this first English edition, the author has updated and significantly expanded the fourth German edition. New additions include the development of apps, graphical presentation on the web, geodata-bases and recent methods of classification. This book is based on the original German 4th edition Geoinformatik in Theorie und Praxis by Norbert de Lange, published by Springer-Verlag GmbH Germany, part of Springer Nature in 2020 and still presents the only integrated perspective on geoinformatics and geoinformation science. This book was translated with the help of artificial intelligence (machine translation by the service DeepL.com) first and then significantly revised with regard to technical terms and special topics of geoinformatics.

This book is entirely devoted to sampled-data control systems analysis and design from a new point of view, which has at its core a mathematical tool named Differential Linear Matrix Inequality - DLMI, a natural generalization of Linear Matrix Inequality - LMI, that had an important and deep impact on systems and control theory almost thirty years ago. It lasts until now. It is shown that the DLMI is well adapted to deal with the important class of sampled-data control systems in both theoretical and numerical contexts. All design conditions are expressed by convex programming problems, including when robustness against parameter uncertainty is assessed and imposed through state feedback control.Special attention is given to filter, dynamic output feedback and model predictive control design, as well as nonlinear systems of Lur¿e class and Markov jump linear systems. The subject is treated with mathematical rigor, at the same time, trying to keep the reading agreeable and fruitful for colleagues and students. To this respect, the book contains together with the theoretical developments, many solved illustrative examples and the formulation of some open problems that could be faced and hopefully solved by interested readers.

The book provides readers with a snapshot of recent research and industrial trends in field of industrial acoustics and vibration. Each chapter, accepted after a rigorous peer-review process, reports on a selected, original piece of work presented and discussed at the Fourth International Conference on Acoustics and Vibration (ICAV2022), which was organized by the Tunisian Association of Industrial Acoustics and Vibration (ATAVI) and held in hybrid format on December 19¿21, 2022, in and from Sousse, Tunisia. The contributions cover advances in both theory and practice in a variety of subfields, such as structural and machine dynamics and vibrations, fault diagnosis and prognosis, nonlinear dynamics, and vibration control of mechatronic systems. Further topics include fluid¿structure interaction, computational vibro-acoustics, vibration field measurements, and dynamic behavior of materials. This book provides a valuable resource for both academics and professionals dealing with diverse issues in applied mechanics. By combining advanced theories with industrial issues, it is expected to facilitate communication and collaboration between different groups of researchers and technology users.