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Infinite horizon autonomous systems with unbounded cost. (English) Zbl 0591.93039
The authors consider time-invariant and periodic control systems defined in an infinite time horizon. The optimal cost functions typically are unbounded as the time tends to infinity. Under certain lower semicontinuity and controllability assumptions it is shown that a linear expression can be subtracted from the cost functional so that the problem reduces to one with bounded costs. For ordinary differential equations with discounted cost functionals, optimality results are determined. Two application examples are presented.
Reviewer: A.Zinober

MSC:
93C99 Model systems in control theory
49J15 Existence theories for optimal control problems involving ordinary differential equations
93B05 Controllability
93B03 Attainable sets, reachability
93C15 Control/observation systems governed by ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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