Utilization of Parametric Programming and Evolutionary Computing in Optimal Control
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Beschreibung
We consider optimal control problems in ODEs from the point of view of parametric optimization and compare the resulting first and second order sweeping methods with approaches from evolutionary comparison. This comparison was suggested as part of the dissertation topic by the Egyptian ministry of higher education. Overall the methods based on classical calculus proved to be more efficient and accurate. According to Pontryagin’s maximum principle the Hamiltonian function must be optimized by the control variables at all points along the solution trajectory. Rather than assuming that these finite dimensional optimization problems are so simple in nature that they can be solved in closed form, they are treated in this thesis as a parametric family with the parameter representing the time of the underlying evolution equation. The resulting control function can have kinks, jumps and singular arcs, which correspond to the singularities of the parametric optimization problem. In this thesis, the only smooth case has been analyzed properly.
We consider optimal control problems in ODEs from the point of view of parametric optimization and compare the resulting first and second order sweeping methods with approaches from evolutionary comparison. This comparison was suggested as part of the dissertation topic by the Egyptian ministry of higher education. Overall the methods based on classical calculus proved to be more efficient and accurate. According to Pontryagin’s maximum principle the Hamiltonian function must be optimized by the control variables at all points along the solution trajectory. Rather than assuming that these finite dimensional optimization problems are so simple in nature that they can be solved in closed form, they are treated in this thesis as a parametric family with the parameter representing the time of the underlying evolution equation. The resulting control function can have kinks, jumps and singular arcs, which correspond to the singularities of the parametric optimization problem. In this thesis, the only smooth case has been analyzed properly.
Autor*in
Amr Radwan
Themen in »Utilization of Parametric Programming and Evolutionary Computing in Optimal Control«
evolutionary computing optimal control parametric optimization