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This open access book gives a systematic introduction into the spectral theory of differential operators on metric graphs. Main focus is on the fundamental relations between the spectrum and the geometry of the underlying graph. The book has two central themes: the trace formula and inverse problems. The trace formula is relating the spectrum to the set of periodic orbits and is comparable to the celebrated Selberg and Chazarain-Duistermaat-Guillemin-Melrose trace formulas. Unexpectedly this formula allows one to construct non-trivial crystalline measures and Fourier quasicrystals solving one of the long-standing problems in Fourier analysis. The remarkable story of this mathematical odyssey is presented in the first part of the book. To solve the inverse problem for Schrödinger operators on metric graphs the magnetic boundary control method is introduced. Spectral data depending on the magnetic flux allow one to solve the inverse problem in full generality, this means to reconstruct not only the potential on a given graph, but also the underlying graph itself and the vertex conditions. The book provides an excellent example of recent studies where the interplay between different fields like operator theory, algebraic geometry and number theory, leads to unexpected and sound mathematical results. The book is thought as a graduate course book where every chapter is suitable for a separate lecture and includes problems for home studies. Numerous illuminating examples make it easier to understand new concepts and develop the necessary intuition for further studies.

Quantum computers. --- Mathematical analysis. --- System theory. --- Control theory. --- Mathematical optimization. --- Calculus of variations. --- Quantum Computing. --- Analysis. --- Systems Theory, Control . --- Calculus of Variations and Optimization.

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This book highlights recent developments in mathematical control theory and its applications to finance. It presents a collection of original contributions by distinguished scholars, addressing a large spectrum of problems and techniques. Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, ranging from "pure" areas of mathematics up to applied sciences like finance. Stochastic optimal control is a well established and important tool of mathematical finance. Other branches of control theory have found comparatively less applications to financial problems, but the exchange of ideas and methods has intensified in recent years. This volume should contribute to establish bridges between these separate fields. The diversity of topics covered as well as the large array of techniques and ideas brought in to obtain the results make this volume a valuable resource for advanced students and researchers.

Control theory. --- Finance --- Mathematical models. --- Dynamics --- Machine theory --- Finance. --- System theory. --- Quantitative Finance. --- Finance, general. --- Systems Theory, Control. --- Funding --- Funds --- Economics --- Currency question --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Systems theory. --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Mathematics --- Methodology

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This open access brief introduces the basic principles of control theory in a concise self-study guide. It complements the classic texts by emphasizing the simple conceptual unity of the subject. A novice can quickly see how and why the different parts fit together. The concepts build slowly and naturally one after another, until the reader soon has a view of the whole. Each concept is illustrated by detailed examples and graphics. The full software code for each example is available, providing the basis for experimenting with various assumptions, learning how to write programs for control analysis, and setting the stage for future research projects. The topics focus on robustness, design trade-offs, and optimality. Most of the book develops classical linear theory. The last part of the book considers robustness with respect to nonlinearity and explicitly nonlinear extensions, as well as advanced topics such as adaptive control and model predictive control. New students, as well as scientists from other backgrounds who want a concise and easy-to-grasp coverage of control theory, will benefit from the emphasis on concepts and broad understanding of the various approaches.

Engineering. --- System theory. --- Mathematical physics. --- Biomathematics. --- Control engineering. --- Control. --- Systems Theory, Control. --- Mathematical and Computational Biology. --- Mathematical Applications in the Physical Sciences. --- Financial Mathematics. --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Biology --- Mathematics --- Physical mathematics --- Physics --- Systems, Theory of --- Systems science --- Science --- Construction --- Industrial arts --- Technology --- Philosophy --- Systems theory. --- Finance—Mathematics. --- Control and Systems Theory. --- Finance --- Mathematics. --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Itinerario de Automática (70884203) --- Bibliografía recomendada --- Control Theory --- Wolfram Mathematica Software --- Robust Control --- Engineering Design Tradeoffs --- Feedback Control Systems --- Optimal Control --- Control theory. --- Social sciences --- Systems Theory, Control . --- Mathematical Physics. --- Mathematics in Business, Economics and Finance. --- Dynamics --- Machine theory

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This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems. Contents: Classical Abstract Spaces in Functional Analysis Linear Functionals and Linear Operators Common Function Spaces in Applications Differential Calculus in Normed Vector Spaces Minimization of Functionals Convex Functionals Lower Semicontinuous Functionals.

Functional analysis. --- Convex functions. --- Mathematical optimization. --- Existence theorems. --- Differential equations --- Mathematical physics --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Functions, Convex --- Functions of real variables --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- System theory. --- Systems Theory, Control. --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Systems theory.

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The transfer function approach is widely used in classical control theory for its easy handling and physical meaning. Although the use of transfer functions is well-established for linear time-invariant systems, it is not suitable for non-stationary systems among which are sampled-data systems and processes with periodically varying coefficients. Computer-controlled continuous-time processes are a very important subset of periodic sampled-data systems which are not treatable using ordinary transfer functions. Having established the ability of the parametric transfer function to solve this problem for single-input, single-output systems in previous work, the authors extend these methods, which incorporate time-dependence, to the idea of the parametric transfer matrix in a complete exposition of analysis and design methods for multiple-input, multiple-output (MIMO) sampled-data systems. Multivariable Computer-controlled Systems is divided into three parts: • Preliminary algebraic material describing the established fundamentals of polynomial and rational matrices necessary for the understanding of later chapters. • Control problems, important in their own right but which also have a substantial bearing on what follows (eigenvalue assignment and the use of z- and zeta-transforms in discrete systems). • Frequency methods for the investigation of MIMO sampled-data systems (parametric discrete-time models; stability; stochastic methods; H2 optimization and L2 design). Appendices covering basic mathematical formulae and the description of two MATLAB® toolboxes round out this self-contained guide to multivariable control systems. Of special interest to researchers in automatic control and to development engineers working with advanced control technology, Multivariable Computer-controlled Systems will also interest mathematical control theorists and graduate students studying advanced methods of computer-based control.

Automatic control. --- Engineering. --- Construction --- Industrial arts --- Technology --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- System theory. --- Computer engineering. --- Control, Robotics, Mechatronics. --- Systems Theory, Control. --- Electrical Engineering. --- Systems, Theory of --- Systems science --- Science --- Computers --- Philosophy --- Design and construction --- Systems theory. --- Control engineering. --- Robotics. --- Mechatronics. --- Electrical engineering. --- Electric engineering --- Engineering --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Machine theory