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Mathematical methods of optimal control theory and their applications
Felixová, Lucie ; Tomášek, Petr (oponent) ; Čermák, Jan (vedoucí práce)
This master's thesis deals with the continuous optimal control problem, which is one of the most important applications of the dierential equations theory. The aim of this work was to study the mathematical theory of the optimal control and the signicant part was to show how Pontryagin's maximum principle and Bellman's principle of optimality can be used in the particular optimal control problems. The emphasis was mainly put on the time and energy ecient electrically powered train control problem, where the quadratic resistant function has been involved.
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The problem of energy-efficient train control
Berkessa, Zewude Alemayehu ; Kisela, Tomáš (oponent) ; Čermák, Jan (vedoucí práce)
The Diploma thesis deals with the problem of energy-efficient train control. It presents the basic survey of mathematical models used in the problem of energy-efficient train control, analysis of optimal driving regimes, determining optimal switching times between optimal driving regimes and timetabling of the train. The mathematical formulation of the problem is done using Newton's second law of motion and other known physical laws. To analyse optimal driving regimes and determine the switching times between optimal driving regimes, we apply tools of optimal control theory, particularly Pontryagin's Maximum Principle. The timetabling of the train is discussed from the numerical solution of the settled non-linear programming problem.
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The problem of energy-efficient train control
Berkessa, Zewude Alemayehu ; Kisela, Tomáš (oponent) ; Čermák, Jan (vedoucí práce)
The Diploma thesis deals with the problem of energy-efficient train control. It presents the basic survey of mathematical models used in the problem of energy-efficient train control, analysis of optimal driving regimes, determining optimal switching times between optimal driving regimes and timetabling of the train. The mathematical formulation of the problem is done using Newton's second law of motion and other known physical laws. To analyse optimal driving regimes and determine the switching times between optimal driving regimes, we apply tools of optimal control theory, particularly Pontryagin's Maximum Principle. The timetabling of the train is discussed from the numerical solution of the settled non-linear programming problem.
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Mathematical methods of optimal control theory and their applications
Felixová, Lucie ; Tomášek, Petr (oponent) ; Čermák, Jan (vedoucí práce)
This master's thesis deals with the continuous optimal control problem, which is one of the most important applications of the dierential equations theory. The aim of this work was to study the mathematical theory of the optimal control and the signicant part was to show how Pontryagin's maximum principle and Bellman's principle of optimality can be used in the particular optimal control problems. The emphasis was mainly put on the time and energy ecient electrically powered train control problem, where the quadratic resistant function has been involved.
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