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This book introduces optimal control problems for large families of deterministic and stochastic systems with discrete or continuous time parameter. These families include most of the systems studied in many disciplines, including Economics, Engineering, Operations Research, and Management Science, among many others. The main objective is to give a concise, systematic, and reasonably self contained presentation of some key topics in optimal control theory. To this end, most of the analyses are based on the dynamic programming (DP) technique. This technique is applicable to almost all control problems that appear in theory and applications. They include, for instance, finite and infinite horizon control problems in which the underlying dynamic system follows either a deterministic or stochastic difference or differential equation. In the infinite horizon case, it also uses DP to study undiscounted problems, such as the ergodic or long-run average cost. After a general introduction to control problems, the book covers the topic dividing into four parts with different dynamical systems: control of discrete-time deterministic systems, discrete-time stochastic systems, ordinary differential equations, and finally a general continuous-time MCP with applications for stochastic differential equations. The first and second part should be accessible to undergraduate students with some knowledge of elementary calculus, linear algebra, and some concepts from probability theory (random variables, expectations, and so forth). Whereas the third and fourth part would be appropriate for advanced undergraduates or graduate students who have a working knowledge of mathematical analysis (derivatives, integrals, ...) and stochastic processes.

Stochastic processes --- mathematische modellen

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Mathematical analysis --- Fourierreeksen --- mathematische modellen

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Mathematics --- mathematics --- mathematische modellen --- wiskunde

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Optimization: Structure and Applications presents selected contributions from renowned researchers in the fields of operations research and industrial engineering. The text is divided into two parts: the first focuses on mathematical structure, and the second, on real-world applications. The book includes recent developments in several optimization-related topics such as decision theory, linear programming, turnpike theory, duality theory, convex analysis, and queueing theory. The applications presented include, but are not limited to, data imaging, network capacity allocation, water system management, and materials design. The 21 self-contained chapters in this volume are devoted to the examination of modern trends and open problems in the field of optimization. This book will be a valuable tool not only to specialists interested in the technical detail and various applications presented, but also to researchers interested in building upon the book's theoretical results.

Planning (firm) --- Computer. Automation --- automatisering --- mathematische modellen

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This book contains geometrical and thermodynamical issues indispensable for development of a rational theory of thermoviscoplasticity. Geometrical picture of coupled thermomagnetomechanical histories of damaged solids is built both by means of Kroener's incompatibility approach as well by Eshelbian implanting eigenstrains. Duality of Euclidean anholonomic and non-Euclidean natural state space is also outlined in this book. Damaged inelastic materials of differential type, discrete and infinitesimal memory are obtained from principle of thermo-inelastic memory. Issue of plastic spin is considered. Postulate of minimal plastic work and corresponding non-associativity 4-tensor are then used to show whether associativity of flow rule holds. Postulates of Drucker, Iliushin and Hill are discussed. Thermodynamics of inelasticity is extensively discussed in classical, rational, extended and endochronic version with account to statistical thermodynamics. A non-steady aging is used in endochronic thermodynamics to cover creep-pasticity coupled inelastic histories. Multiaxial dynamic experiments with cylindrical, ``bichierino'' and cruciform specimen from austenitic stainless steels are analyzed. Quasi-rate independence and Rabotnov's plastic delay is combined with tensor representation. Inelastic ferromagnetics are treated by means of extended as well endochronic thermodynamics. For low cycle fatigue the experimentally observed displacement of magnetic induction history with respect to stress history is analyzed. Self consistent method applied to inelastic polycrystals is based on constrained micro-rotations and free meso-rotations. A special attention is devoted to slight disorder of polycrystal grains. The theory is confronted with classical J2-theory. Different inelastic multiaxial stress histories are analyzed and corresponding active slip systems determined. For numerical results micro quasi rate independence and relaxed Taylor's model are used. The theory of inelastic micromorphic polycrystals with couple stresses needs a very small number of necessary material constants. Nonproportionality of strain history as well as intergranular continuity are related to antisymmetry of stress tensor. Key topics: * Includes a detailed description of the geometry of thermo-deformation with local evolving natural state configuration * Provides a comparative review of various models of thermodynamics (classical, rational, endochronic, statistical) with special approach to inelastic high speed histories * Introduces quasi-rate independence and its application to plastic waves, ratcheting, and diffuse localization * Explores the sensor representation approach to thermo-inelastic coupled fields connected to a generalized associativity of flow rule as well as a comparison with the J2-approach * Examines micromechanics based on micro grain approach leading to reduced number of material constants * Provides biaxial cruciform specimen Hopkinson bar results * Reexamines the Hill's yield function for nonproportional stress-thermo-strain histories This book is intended for material science experts and professionals interested in impact experiments, continuum mechanics researchers, engineers in research institutes and graduate and Phd students aiming to apply FEM to calculate strength of structures at time varying thermo-mechanical excitations.

Fluid mechanics --- Planning (firm) --- mathematische modellen --- mechanica