Stratifiable Families of Extremals and Sufficient Conditions for Optimality in Optimal Control Problems

U. Ledzewicz, A. Nowakowski and H. Schättler
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U. Ledzewicz: Southern Illinois University at Edwardsville
A. Nowakowski: Institute of Mathematics, University of Łódź, Łódź
H. Schättler: Washington University

Journal of Optimization Theory and Applications, 2004, vol. 122, issue 2, No 6, 345-370

Abstract: 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 (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOTA.0000042525.50701.9a

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