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Asymptotic properties of optimal solutions in planar discounted control problems. (English) Zbl 0688.49038
The author considers optimal control problems on (0,\(\infty)\) with a discount factor where the performance index does not depend explicitly on the control and the system is linear in the control and has the “ecological form”. The main result is a generalization of the classical Poincaré-Bendixson theorem: For every optimal pair the “omega limit set” is either the trajectory of a periodic trajectory or the union of trajectories connecting optimal equilibria.
Reviewer: A.Kirsch

49M99 Numerical methods in optimal control
34C25 Periodic solutions to ordinary differential equations
92D25 Population dynamics (general)
49J99 Existence theories in calculus of variations and optimal control
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