Article ID Journal Published Year Pages File Type
6419074 Journal of Mathematical Analysis and Applications 2012 18 Pages PDF
Abstract

We consider a general class of infinite-horizon optimization problems, where the phase space is a two dimensional manifold satisfying the Jordan curve theorem, and the set of feasible curves satisfies general conditions similar to, but weaker than the solution set of a control system. We verify the existence of an optimal periodic solution for this class of problems. Applying this result we obtain two new results: we generalize a previous result for discounted infinite-horizon control problems, and provide a Poincaré-Bendixson type result for continuous generalized semi-flows.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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