Asymptotic properties of optimal solutions in planar discounted control problems. (English) Zbl 0688.49038

Colonius, Fritz; Sieveking, Malte

SIAM J. Control Optimization 27, No. 3, 608-630 (1989).

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

MSC:

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

Keywords:

infinite horizon optimal control; optimal resource management; Poincaré-Bendixson theorem