Geodesic
On the boundedness of optimal controls in infinite-horizon problems
Informatics and Automation, Optimal control, Tome 291 (2015), pp. 45-55.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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S. M. Aseev. On the boundedness of optimal controls in infinite-horizon problems. Informatics and Automation, Optimal control, Tome 291 (2015), pp. 45-55. http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a3/

[1] Acemoglu D., Introduction to modern economic growth, Princeton Univ. Press, Princeton, NJ, 2008

[2] Alekseev V.M., Tikhomirov V.M., Fomin S.V., Optimalnoe upravlenie, Nauka, M., 1979 | MR

[3] Aseev S.M., “Sopryazhennye peremennye i mezhvremennye tseny v zadachakh optimalnogo upravleniya na beskonechnom intervale vremeni”, Tr. MIAN, 290 (2015), 239–253

[4] Aseev S., Besov K., Kaniovski S., “The problem of optimal endogenous growth with exhaustible resources revisited”, Green growth and sustainable development, Dyn. Model. Econometr. Econ. Finance, 14, Springer, Berlin, 2013, 3–30 | DOI | MR

[5] Aseev S.M., Besov K.O., Kryazhimskii A.V., “Zadachi optimalnogo upravleniya na beskonechnom intervale vremeni v ekonomike”, UMN, 67:2 (2012), 3–64 | DOI | MR | Zbl

[6] Aseev S.M., Kryazhimskiy A.V., “The Pontryagin maximum principle and transversality conditions for a class of optimal control problems with infinite time horizons”, SIAM J. Control Optim., 43:3 (2004), 1094–1119 | DOI | MR | Zbl

[7] Aseev S.M., Kryazhimskii A.V., Printsip maksimuma Pontryagina i zadachi optimalnogo ekonomicheskogo rosta, Tr. MIAN, 257, Nauka, M., 2007 | MR | Zbl

[8] Aseev S.M., Veliov V.M., “Needle variations in infinite-horizon optimal control”, Variational and optimal control problems on unbounded domains, Contemp. Math., 619, Ed. by G. Wolansky, A.J. Zaslavski, Amer. Math. Soc., Providence, RI, 2014, 1–17 | DOI | MR

[9] Aseev S.M., Veliov V.M., “Maximum principle for infinite-horizon optimal control problems under weak regularity assumptions”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20:3 (2014), 41–57 | MR

[10] Balder E.J., “An existence result for optimal economic growth problems”, J. Math. Anal. Appl., 95 (1983), 195–213 | DOI | MR | Zbl

[11] Barro R.J., Sala-i-Martin X., Economic growth, McGraw Hill, New York, 1995

[12] Besov K.O., “O neobkhodimykh usloviyakh optimalnosti dlya zadach ekonomicheskogo rosta s beskonechnym gorizontom i lokalno neogranichennoi funktsiei mgnovennoi poleznosti”, Tr. MIAN, 284 (2014), 56–88 | Zbl

[13] Carlson D.A., Haurie A.B., Leizarowitz A., Infinite horizon optimal control: Determenistic and stochastic systems, Springer, Berlin, 1991 | MR

[14] Cesari L., Optimization—theory and applications. Problems with ordinary differential equations, Springer, New York, 1983 | MR | Zbl

[15] Clarke F.H., Vinter R.B., “Regularity properties of optimal controls”, SIAM J. Control Optim., 28:4 (1990), 980–997 | DOI | MR | Zbl

[16] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR

[17] Hotelling H., “The economics of exhaustible resources”, J. Polit. Econ., 39:2 (1931), 137–175 | DOI | MR | Zbl

[18] Manzoor T., Aseev S., Rovenskaya E., Muhammad A., “Optimal control for sustainable consumption of natural resources”, Proc. 19th IFAC World Congr., 2014, Ed. by E. Boje, X. Xia, Int. Fed. Autom. Control, Laxenburg, 2014, 10725–10730

[19] Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mischenko E.F., Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961

[20] Sarychev A.V., Torres D.F.M., “Lipschitzian regularity of minimizers for optimal control problems with control-affine dynamics”, Appl. Math. Optim., 41:2 (2000), 237–254 | DOI | MR | Zbl

[21] Tarasev A.M., Usova A.A., Wang W., Russkikh O.V., “Postroenie optimalnykh traektorii integrirovaniem gamiltonovoi dinamiki v modelyakh ekonomicheskogo rosta pri resursnykh ogranicheniyakh”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20:4 (2014), 258–276 | MR

[22] Torres D.F.M., “Regularity of minimizers in optimal control”, Equadiff 10: Proc. Czech. Int. Conf. on Differential Equations and Their Applications, Part 2 (Prague, 2001), Ed. by J. Kuben, J. Vosmanský, Masaryk Univ., Brno, 2002, 397–412

[23] Valente S., “Sustainable development, renewable resources and technological progress”, Environ. Resour. Econ., 30 (2005), 115–125 | DOI

[24] Zaslavski A.J., “Existence and uniform boundedness of optimal solutions of variational problems”, Abstr. Appl. Anal., 3:3–4 (1998), 265–292 | DOI | MR