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Stratifiable Families of Extremals and Sufficient Conditions for Optimality in Optimal Control Problems |
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| Authors: | Ledzewicz U. Nowakowski A. Schättler H. |
| Affiliation: | 1.Professor, Department of Mathematics and Statistics, Southern Illinois University at Edwardsville, Edwardsville, Illinois, U.S.A ;2.Professor, Institute of Mathematics, University of ?ód?, ?ód?, Poland ;3.Associate Professor, Department of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, U.S.A ; |
| Abstract: | It is shown that, if a parametrized fämily of extremals F can be stratified in a way compatible with the flow map generated by F, then those trajectories of the family which realize the minimal values of the cost in F are indeed optimal in comparison with all trajectories which lie in the region R covered by the trajectories of F. It is not assumed that F is a field covering the state space injectively. As illustration, an optimal synthesis is constructed for a system where the flow of extremals exhibits a simple cusp singularity. |
| Keywords: | Optimal control field theory method of characteristics singularities strong local minima |
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