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This book is based on lectures from a one-year course at the Far Eastern Federal University (Vladivostok, Russia) as well as on workshops on optimal control offered to students at various mathematical departments at the university level. The main themes of the theory of linear and nonlinear systems are considered, including the basic problem of establishing the necessary and sufficient conditions of optimal processes. In the first part of the course, the theory of linear control systems is constructed on the basis of the separation theorem and the concept of a reachability set. The authors prove the closure of a reachability set in the class of piecewise continuous controls, and the problems of controllability, observability, identification, performance and terminal control are also considered. The second part of the course is devoted to nonlinear control systems. Using the method of variations and the Lagrange multipliers rule of nonlinear problems, the authors prove the Pontryagin maximum principle for problems with mobile ends of trajectories. Further exercises and a large number of additional tasks are provided for use as practical training in order for the reader to consolidate the theoretical material.
Mathematics. --- System theory. --- Calculus of variations. --- Calculus of Variations and Optimal Control; Optimization. --- Systems Theory, Control. --- Mathematical optimization. --- Systems theory. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Control theory. --- Systems, Theory of --- Systems science --- Science --- Isoperimetrical problems --- Variations, Calculus of --- Philosophy
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Mathematical optimization. --- Calculus of variations. --- System theory. --- Systems, Theory of --- Systems science --- Science --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- Philosophy --- Optimització matemàtica --- Càlcul de variacions --- Teoria de sistemes --- Filosofia de la ciència --- Anàlisi de sistemes --- Autopoesi --- Caos (Teoria de sistemes) --- Enginyeria de sistemes --- Sistemes biològics --- Sistemes complexos --- Sistemes lineals --- Sistemes no lineals --- Sistemes socials --- Càlcul variacional --- Problemes isoperimètrics --- Màxims i mínims --- Anàlisi funcional --- Desigualtats variacionals (Matemàtica) --- Dominis convexos --- Equacions de Hamilton-Jacobi --- Funcions de Lagrange --- Principis variacionals --- Teoria de Morse --- Teoria del punt crític (Anàlisi matemàtica) --- Mètodes de simulació --- Jocs d'estratègia (Matemàtica) --- Optimització combinatòria --- Programació dinàmica --- Programació (Matemàtica)
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This book is based on lectures from a one-year course at the Far Eastern Federal University (Vladivostok, Russia) as well as on workshops on optimal control offered to students at various mathematical departments at the university level. The main themes of the theory of linear and nonlinear systems are considered, including the basic problem of establishing the necessary and sufficient conditions of optimal processes. In the first part of the course, the theory of linear control systems is constructed on the basis of the separation theorem and the concept of a reachability set. The authors prove the closure of a reachability set in the class of piecewise continuous controls, and the problems of controllability, observability, identification, performance and terminal control are also considered. The second part of the course is devoted to nonlinear control systems. Using the method of variations and the Lagrange multipliers rule of nonlinear problems, the authors prove the Pontryagin maximum principle for problems with mobile ends of trajectories. Further exercises and a large number of additional tasks are provided for use as practical training in order for the reader to consolidate the theoretical material.
Functional analysis --- Numerical methods of optimisation --- Mathematics --- Engineering sciences. Technology --- analyse (wiskunde) --- systeemtheorie --- wiskunde --- systeembeheer --- kansrekening --- optimalisatie
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