Geodesic
On the boundedness of optimal controls in infinite-horizon problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 291 (2015), pp. 45-55

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A class of infinite-horizon optimal control problems that arise in economic applications is considered. A theorem on the nonemptiness and boundedness of the set of optimal controls is proved by the method of finite-horizon approximations and the apparatus of the Pontryagin maximum principle. As an example, a simple model of optimal economic growth with a renewable resource is considered. 
@article{TM_2015_291_a3,
     author = {S. M. Aseev},
     title = {On the boundedness of optimal controls in infinite-horizon problems},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {45--55},
     publisher = {mathdoc},
     volume = {291},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2015_291_a3/}
}
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S. M. Aseev. On the boundedness of optimal controls in infinite-horizon problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 291 (2015), pp. 45-55. http://geodesic.mathdoc.fr/item/TM_2015_291_a3/