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Differential equations --- Differential inclusions --- Fixed point theory --- Numerical solutions --- Congresses --- Differential equations - Numerical solutions - Congresses --- Differential inclusions - Congresses --- Fixed point theory - Congresses

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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 --- Automatic control.