# zbMATH — the first resource for mathematics

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
Full Text:
##### References:
 [1] Bellman R, Bucy R (1964) Asymptotic control theory. SIAM Control 2:11-18 · Zbl 0132.38101 [2] Brock WA, Haurie A (1976) On existence of overtaking optimal trajectories over an infinite time horizon. Math Op Res 1:337-346 · Zbl 0367.49003 · doi:10.1287/moor.1.4.337 [3] Gale D (1967) On optimal development in a multi-sector economy. Rev Econ Studies 34:1-19 · doi:10.2307/2296567 [4] Rockefellar RT (1979) Convex processes and Hamiltonian dynamical systems. In: Krein J (ed) Convex Analysis and Mathematical Economics. Lecture Notes in Economics and Mathematical Systems 168:122-136 [5] Rudin W (1974) Real and Complex Analysis. McGraw-Hill Series in Higher Mathematics. New York, McGraw-Hill [6] von Weizsacker CC (1965) Existence of optimal programs of accumulation for an infinite horizon. Rev Econ Studies 32:85-104 · doi:10.2307/2296054
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.