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Lecturer(s)
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Cvejn Jan, doc. Ing. Ph.D.
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Course content
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Problems of dynamic optimization in discrete time domain - transformation into static optimization problem, Bellman optimality principle. Variational approach to solving problems in continuous domain, necessary and sufficient conditions of the extreme. HBJ equation. Applications for linear systems, LQR controller. Solving problems with contraints on control and state, Pontrjagin maximum principle. Numerical methods of computation of optimal trajectories. Introduction into modern mathematical theory of optimal processes - basics of differential calculus in functional spaces and their applications for obtaining conditions of optimality.
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Learning activities and teaching methods
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Work with text (with textbook, with book)
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Learning outcomes
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The subject is focused on introduction into basics of deterministic theory of optimal processes and principles of numerical solving extremal tasks with respect to applications in the area of technological processes.
Obtaining orientation in the basics of deterministic theory of optimal processes and in principles of numerical solving extremal tasks with respect to applications in the area of technological processes.
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Prerequisites
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Knowledge of differential and integral calculus, linear algebra and fundamentals of control theory.
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Assessment methods and criteria
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Oral examination
Examination
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Recommended literature
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Alexejev V. M. a kol. Matematická teorie optimálních procesů. Academia, Praha, 1991.
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Bryson A. E., Ho Y.C. Applied Optimal Control . Hemisphere Corp., New York, 1981.
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Kirk, D.E. Optimal Control Theory: An Introduction. Dover Publications, 2004.
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Stengel, R. Optimal Control and Estimation. Dover Publications, 1994.
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Štecha J. Optimální rozhodování a řízení. ČVUT, Praha, 2000.
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