Structure of solutions of nonautonomous optimal control problems in metric spaces

• Autorzy: Zaslavski A. J.

Identyfikatory

DOI

10.7862/rf.2015.12

• Języki publikacji: EN

Abstrakty

EN

We establish turnpike results for a nonautonomous discrete-time optimal control system describing a model of economic dynamics.

Słowa kluczowe

EN

compact metric space; infinite horizon problem; optimization; turnpike property

PL

przestrzeń metryczna; horyzont nieskończony; optymalizacja; sterowanie optymalne

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2015
• Tom: Vol. 38
• Strony: 151--169
• Opis fizyczny: Bibliogr. 32 poz.

Twórcy

autor

Zaslavski A. J.

• Department of Mathematics, Technion-Israel Institute of Technology, 32000, Haifa, Israel

Bibliografia

• [1] B. D. O. Anderson and J. B. Moore Linear optimal control Prentice-Hall, Englewood Cliffs, NJ 1971
• [2] S. M. Aseev, K. O. Besov and A. V. Kryazhimskii Infinite-horizon optimal control problems in economics, Russ. Math. Surv. 67, (2012), 195-253
• [3] S. Aubry and P. Y. Le Daeron The discrete Frenkel-Kontorova model and its extensions I Physica D 8 (1983), 381-422
• [4] J. Baumeister, A. Leitao and G. N. Silva On the value function for nonautonomous optimal control problem with infinite horizon Systems Control Lett. 56, 188-196 (2007).
• [5] J. Blot Infinite-horizon Pontryagin principles without invertibility J. Nonlinear Convex Anal. 10 (2009), 177-189.
• [6] J. Blot and P. Cartigny Optimality in infinite-horizon variational problems under sign conditions J. Optim. Theory Appl. 106, 411-419 (2000).
• [7] J. Blot and N. Hayek Sufficient conditions for infinite-horizon calculus of variations problems ESAIM Control Optim. Calc. Var. 5 (2000), 279-292.
• [8] P. Cartigny and P. Michel On a sufficient transversality condition for infinite horizon optimal control problems Automatica J. IFAC 39 (2003), 1007-1010.
• [9] D. Gale On optimal development in a multi-sector economy Review of Economic Studies 34, 1-18 (1967).
• [10] N. Hayek Infinite horizon multiobjective optimal control problems in the discrete time case Optimization 60 (2011), 509-529.
• [11] H. Jasso-Fuentes and O. Hernandez-Lerma Characterizations of overtaking optimality for controlled diffusion processes Appl. Math. Optim. 57 (2008), 349-369.
• [12] A. Leizarowitz Infinite horizon autonomous systems with unbounded cost Appl. Math. and Opt. 13 (1985), 19-43.
• [13] A. Leizarowitz and V. J. Mizel One dimensional infinite horizon variational problems arising in continuum mechanics Arch. Rational Mech. Anal. 106 (1989), 161-194.
• [14] V. Lykina, S. Pickenhain andM.Wagner Different interpretations of the improper integral objective in an infinite horizon control problem J. Math. Anal. Appl. 340 (2008), 498-510.
• [15] A. B. Malinowska, N. Martins and D. F. M. Torres Transversality conditions for infinite horizon variational problems on time scales Optim. Lett. 5 (2011), 41-53.
• [16] M. Marcus and A. J. Zaslavski The structure of extremals of a class of second order variational problems Ann. Inst. H. Poincare, Anal. non lineare 16, 593-629 (1999).
• [17] L. W. McKenzie Turnpike theory Econometrica 44 (1976), 841-866.
• [18] B. Mordukhovich Optimal control and feedback design of state-constrained parabolic systems in uncertainly conditions Appl. Analysis 90 (2011), 1075-1109
• [19] B. Mordukhovich and I. Shvartsman Optimization and feedback control of constrained parabolic systems under uncertain perturbations Optimal Control, Stabilization and Nonsmooth Analysis, Lecture Notes Control Inform. Sci.(2004), Springer, 121-132.
• [20] E. Ocana and P. Cartigny Explicit solutions for singular infinite horizon calculus of variations SIAM J. Control Optim. 50(2012), 2573-2587.
• [21] E. Ocana, P. Cartigny and P. Loisel Singular infinite horizon calculus of variations. Applications to fisheries management J. Nonlinear Convex Anal. 10 (2009), 157-176.
• [22] S. Pickenhain, V. Lykina and M.WagnerOn the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems Control Cybernet. 37 (2008), 451-468.
• [23] T. Prieto-Rumeau and O. Hernandez-Lerma Bias and overtaking equilibria for zero-sum continuous-time Markov games Math. Methods Oper. Res. 61 (2005), 437-454.
• [24] A.M. Rubinov Economic dynamics J. Soviet Math. 26 (1984), 1975-2012.
• [25] P. A. Samuelson A catenary turnpike theorem involving consumption and the golden rule American Economic Review 55 (1965), 486-496.
• [26] A. J. Zaslavski Ground states in Frenkel-Kontorova model Math. USSR Izvestiya 29 (1987), 323-354.
• [27] A. J. Zaslavski Turnpike properties in the calculus of variations and optimal control Springer, New York, 2006.
• [28] A. J. Zaslavski Turnpike results for a discrete-time optimal control system arising in economic dynamics Nonlinear Analysis 67, (2007) 2024-2049.
• [29] A. J. Zaslavski Two turnpike results for a discrete-time optimal control system Nonlinear Analysis 71, (2009) 902-909 .
• [30] A. J. Zaslavski Structure of solutions of variational problems. SpringerBriefs in Optimization, Springer, New York 2013.
• [31] A. J. Zaslavski Necessary and sufficient conditions for turnpike properties of solutions of optimal control systems arising in economic dynamics Dynamics of Continuous, Discrete and Impulsive Systems, Ser. B Appl. Algorithms 20 (2013), 391-420.
• [32] A. J. Zaslavski and A. Leizarowitz Optimal solutions of linear control systems with nonperiodic integrands Mathematics of Operations Research 22 (1997), 726-746.