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Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions. In addition to including well-recognized results of variational analysis and optimization, the book includes a number of new and important onesIncludes practical examples

Approximation theory. --- Differential inclusions. --- Mathematical optimization. --- Differential inclusions --- Mathematical optimization --- Approximation theory --- Civil & Environmental Engineering --- Mathematics --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Calculus --- Operations Research --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems

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Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory, explaining and motivating the main concepts and  illustrating them with numerous numerical examples taken from various fields.

Differential inclusions. --- Feedback control systems. --- Set-valued maps. --- Differential inclusions --- Set-valued maps --- Feedback control systems --- Mathematics --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Calculus --- Operations Research --- Population viability analysis. --- Analysis, Population viability --- Assessment, Population viability --- Population viability analyses --- Population viability assessment --- PVA (Population viability analysis) --- Viability analysis, Population --- Viability assessment, Population --- Mathematics. --- Computer science --- Game theory. --- System theory. --- Control engineering. --- Economic theory. --- Systems Theory, Control. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Math Applications in Computer Science. --- Control. --- Game Theory, Economics, Social and Behav. Sciences. --- Population biology --- Statistical methods --- Systems theory. --- Computer science. --- Control and Systems Theory. --- Math --- Science --- Informatics --- Economic theory --- Political economy --- Social sciences --- Economic man --- Computer science—Mathematics. --- Games, Theory of --- Theory of games --- Mathematical models --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Systems, Theory of --- Systems science --- Philosophy --- Computer mathematics --- Electronic data processing

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This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.

Mathematics. --- Ordinary Differential Equations. --- Dynamical Systems and Ergodic Theory. --- Systems Theory, Control. --- Differentiable dynamical systems. --- Differential Equations. --- Systems theory. --- Mathématiques --- Dynamique différentiable --- Differential inclusions. --- Functional differential equations. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Inclusions, Differential --- Differential equations, Functional --- Dynamics. --- Ergodic theory. --- Differential equations. --- System theory. --- Differentiable dynamical systems --- Differential equations --- Set-valued maps --- Functional equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- 517.91 Differential equations --- Systems, Theory of --- Systems science --- Science --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Philosophy

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This work examines viability theory and its applications to control theory and differential games. The emphasis is on the construction of feedbacks and dynamical systems by myopic optimization methods. Systems of first-order partial differential inclusions, whose solutions are feedbacks, are constructed and investigated. Basic results are then extended to the case of fuzzy control problems, distributed control problems, and control systems with delays and memory. Aimed at graduate students and research mathematicians, both pure and applied, this book offers specialists in control and nonlinear systems tools to take into account general state constraints. Viability theory also allows researchers in other disciplines—artificial intelligence, economics, game theory, theoretical biology, population genetics, cognitive sciences—to go beyond deterministic models by studying them in a dynamical or evolutionary perspective in an uncertain environment. The book is a compendium of the state of knowledge about viability...Mathematically, the book should be accessible to anyone who has had basic graduate courses in modern analysis and functional analysis…The concepts are defined and many proofs of the requisite results are reproduced here, making the present book essentially self-contained. —Bulletin of the AMS Because of the wide scope, the book is an ideal reference for people encountering problems related to viability theory in their research…It gives a very thorough mathematical presentation. Very useful for anybody confronted with viability constraints. —Mededelingen van het Wiskundig Genootschap.

Differential inclusions. --- Feedback control systems. --- Set-valued maps. --- Differential inclusions --- Set-valued maps --- Feedback control systems --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Feedback mechanisms --- Feedback systems --- Many-valued mappings --- Mappings, Point-to-set --- Maps, Set-valued --- Multi-valued mappings --- Multivalued mappings --- Point-to-set mappings --- Inclusions, Differential --- Inclusions différentielles --- Systèmes à réaction --- Applications multivoques --- Inclusions différentielles --- Systèmes à réaction --- Mathematics. --- Artificial intelligence. --- Game theory. --- System theory. --- Biomathematics. --- Control engineering. --- Robotics. --- Mechatronics. --- Systems Theory, Control. --- Control, Robotics, Mechatronics. --- Game Theory, Economics, Social and Behav. Sciences. --- Mathematical and Computational Biology. --- Artificial Intelligence (incl. Robotics). --- Systems theory. --- Artificial Intelligence. --- Math --- Science --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Automation --- Biology --- Games, Theory of --- Theory of games --- Mathematical models --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Programmable controllers --- Systems, Theory of --- Systems science --- Philosophy

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Stochastic Differential Inclusions and Applications further develops the theory of stochastic functional inclusions and their applications. This self-contained volume is designed to systematically introduce the reader from the very beginning to new methods of the stochastic optimal control theory. The exposition contains detailed proofs and uses new and original methods to characterize the properties of stochastic functional inclusions that, up to the present time, have only been published recently by the author. The text presents recent and pressing issues in stochastic processes, control, differential games, and optimization that can be applied to finance, manufacturing, queueing networks, and climate control. The work is divided into seven chapters, with the first two, containing selected introductory material dealing with point- and set-valued stochastic processes. The final two chapters are devoted to applications and optimal control problems. Written by an award-winning author in the field of stochastic differential inclusions and their application to control theory, this book is intended for students and researchers in mathematics and applications, particularly those studying optimal control theory. It is also highly relevant for students of economics and engineering. The book can also be used as a reference on stochastic differential inclusions. Knowledge of select topics in analysis and probability theory are required.

Mathematics. --- Stochastic partial differential equations. --- Stochastic processes. --- Differential equations --- Differential equations, Partial --- Numerical analysis --- Mathematical optimization --- Mathematics --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Operations Research --- Calculus --- Differential equations. --- Differential equations, Partial. --- Partial differential equations --- 517.91 Differential equations --- Math --- Random processes --- Banach spaces, Stochastic differential equations in --- Hilbert spaces, Stochastic differential equations in --- SPDE (Differential equations) --- Stochastic differential equations in Banach spaces --- Stochastic differential equations in Hilbert spaces --- Partial differential equations. --- Numerical analysis. --- Calculus of variations. --- Calculus of Variations and Optimal Control; Optimization. --- Ordinary Differential Equations. --- Numerical Analysis. --- Partial Differential Equations. --- Science --- Probabilities --- Mathematical optimization. --- Differential Equations. --- Differential equations, partial. --- Mathematical analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Isoperimetrical problems --- Variations, Calculus of --- Stochastic control theory. --- Differential inclusions.