Structure of approximate solutions for a class of optimal control systems

• Autorzy: Zaslavski A. J.
• Języki publikacji: EN

Abstrakty

EN

We study a turnpike property of approximate solutions of a discrete-time control system with a compact metric space of states which arises in economic dynamics. To have this property means that the approximate solutions of the optimal control problems are determined mainly by an objective function, and are essentially independent of the length of the interval, for all sufficiently large intervals. We show that the turnpike property is stable under perturbations of an objective function.

Słowa kluczowe

EN

control system; good function; infinite horizon problem; optimal solution

PL

układ sterujący; horyzont nieskończony; optymalizacja; rozwiązanie optymalne

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2011
• Tom: Vol. 34
• Strony: 135--149
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Zaslavski A. J.

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

Bibliografia

• [1] S. Aubry and P. Y. Le Daeron, The discrete Frenkel-Kontorova model and its extensions I, Physica D 8 (1983), 381-422
• [2] J. Blot and N. Hayek ,Sufficient conditions for infinite-horizon calculus of variations problems, ESAIM Control Optim. Calc. Var. 5 (2000), 279-292
• [3] D. Gale On optimal development in a multi-sector economy, Review of Economic Studies 34 (1967), 1-18
• [4] A. Leizarowitz, Infinite horizon autonomous systems with unbounded cost, Appl. Math. and Opt. 13 (1985), 19-43
• [5] A. Leizarowitz ,Tracking nonperiodic trajectories with the overtaking criterion, Appl. Math. and Opt. 14 (1986), 155-171
• [6] A. Leizarowitz and V. J. Mizel, One dimensional infinite horizon variational problems arising in continuum mechanics, Arch. Rational Mech. Anal. 106 (1989), 161-194
• [7] L. W. McKenzie, Turnpike theory, Econometrica 44 (1976), 841-866
• [8] S. Pickenhain, V. Lykina and M.Wagner, On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems, Control Cybernet. 37 (2008), 451-468
• [9] P. A. Samuelson, A catenary turnpike theorem involving consumption and the golden rule, American Economic Review 55 (1965), 486-496
• [10] A. J. Zaslavski Optimal programs on infinite horizon 1, SIAM Journal on Control and Optimization, 33 (1995), 1643-1660
• [11] A. J. Zaslavski Optimal programs on infinite horizon 2, SIAM Journal on Control and Optimization 33 (1995), 1661-1686
• [12] A. J. Zaslavski Turnpike properties in the calculus of variations and optimal control, Springer New York 2006
• [13] A. J. Zaslavski Turnpike results for a discrete-time optimal control system arising in economic dynamics, Nonlinear Analysis 67 (2007), 2024-2049
• [14] A. J. Zaslavski Two turnpike results for a discrete-time optimal control system, Nonlinear Analysis 71 (2009), 902-909
• [15] A. J .Zaslavski Stability of a turnpike phenomenon for a discrete-time optimal control system, J. Optim. Theory Appl. 145 (2010), 597-612