American Institute of Mathematical Sciences

Advanced
August  2005, 5(3): 861-880. doi: 10.3934/dcdsb.2005.5.861

The turnpike property of discrete-time control problems arising in economic dynamics

Alexander J. Zaslavski 1,

1. 

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

Received  January 2004 Revised  April 2004 Published  May 2005

In this work we study the structure of approximate solutions of a nonautonomous discrete-time control system in a compact metric space $X$ which is determined by a sequence of continuous functions $v_i: X \times X \to R^1$, $i=0,\pm 1,\pm 2,$.... The main result in this paper deals with the turnpike property of optimal control problems. To have this property means that the approximate solutions of the problems are determined mainly by the the sequence $\{v_i\}_{i=-\infty}^{\infty}$, and are essentially independent of the choice of interval and endpoint conditions, except in regions close to the endpoints.
Keywords: good sequence, complete metric space, Compact metric space, generic property, turnpike property..
Mathematics Subject Classification: Primary: 49J99, 54E5.
Citation: Alexander J. Zaslavski. The turnpike property of discrete-time control problems arising in economic dynamics. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 861-880. doi: 10.3934/dcdsb.2005.5.861
[1]

Jaeyoo Choy, Hahng-Yun Chu. On the dynamics of flows on compact metric spaces. Communications on Pure & Applied Analysis, 2010, 9 (1) : 103-108. doi: 10.3934/cpaa.2010.9.103
[2]

Mário Jorge Dias Carneiro, Alexandre Rocha. A generic property of exact magnetic Lagrangians. Discrete & Continuous Dynamical Systems - A, 2012, 32 (12) : 4183-4194. doi: 10.3934/dcds.2012.32.4183
[3]

Alexander J. Zaslavski. Stability of a turnpike phenomenon for a class of optimal control systems in metric spaces. Numerical Algebra, Control & Optimization, 2011, 1 (2) : 245-260. doi: 10.3934/naco.2011.1.245
[4]

Jinjun Li, Min Wu. Generic property of irregular sets in systems satisfying the specification property. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 635-645. doi: 10.3934/dcds.2014.34.635
[5]

Alexander V. Rezounenko, Petr Zagalak. Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 819-835. doi: 10.3934/dcds.2013.33.819
[6]

Zhiming Li, Lin Shu. The metric entropy of random dynamical systems in a Hilbert space: Characterization of invariant measures satisfying Pesin's entropy formula. Discrete & Continuous Dynamical Systems - A, 2013, 33 (9) : 4123-4155. doi: 10.3934/dcds.2013.33.4123
[7]

Jintao Wang, Desheng Li, Jinqiao Duan. On the shape Conley index theory of semiflows on complete metric spaces. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1629-1647. doi: 10.3934/dcds.2016.36.1629
[8]

Shigenori Matsumoto. A generic-dimensional property of the invariant measures for circle diffeomorphisms. Journal of Modern Dynamics, 2013, 7 (4) : 553-563. doi: 10.3934/jmd.2013.7.553
[9]

Hartmut Schwetlick, Daniel C. Sutton, Johannes Zimmer. On the $\Gamma$-limit for a non-uniformly bounded sequence of two-phase metric functionals. Discrete & Continuous Dynamical Systems - A, 2015, 35 (1) : 411-426. doi: 10.3934/dcds.2015.35.411
[10]

Longye Wang, Gaoyuan Zhang, Hong Wen, Xiaoli Zeng. An asymmetric ZCZ sequence set with inter-subset uncorrelated property and flexible ZCZ length. Advances in Mathematics of Communications, 2018, 12 (3) : 541-552. doi: 10.3934/amc.2018032
[11]

Alex Castro, Wyatt Howard, Corey Shanbrom. Complete spelling rules for the Monster tower over three-space. Journal of Geometric Mechanics, 2017, 9 (3) : 317-333. doi: 10.3934/jgm.2017013
[12]

Anton Petrunin. Metric minimizing surfaces. Electronic Research Announcements, 1999, 5: 47-54.

[13]

Valentin Afraimovich, Lev Glebsky, Rosendo Vazquez. Measures related to metric complexity. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1299-1309. doi: 10.3934/dcds.2010.28.1299
[14]

Vincenzo Recupero. Hysteresis operators in metric spaces. Discrete & Continuous Dynamical Systems - S, 2015, 8 (4) : 773-792. doi: 10.3934/dcdss.2015.8.773
[15]

Vladimir Georgiev, Eugene Stepanov. Metric cycles, curves and solenoids. Discrete & Continuous Dynamical Systems - A, 2014, 34 (4) : 1443-1463. doi: 10.3934/dcds.2014.34.1443
[16]

Anton Petrunin. Correction to: Metric minimizing surfaces. Electronic Research Announcements, 2018, 25: 96-96. doi: 10.3934/era.2018.25.010
[17]

Qinian Jin, YanYan Li. Starshaped compact hypersurfaces with prescribed $k$-th mean curvature in hyperbolic space. Discrete & Continuous Dynamical Systems - A, 2006, 15 (2) : 367-377. doi: 10.3934/dcds.2006.15.367
[18]

Kazuhiro Sakai. The oe-property of diffeomorphisms. Discrete & Continuous Dynamical Systems - A, 1998, 4 (3) : 581-591. doi: 10.3934/dcds.1998.4.581
[19]

Pablo Sánchez, Jaume Sempere. Conflict, private and communal property. Journal of Dynamics & Games, 2016, 3 (4) : 355-369. doi: 10.3934/jdg.2016019
[20]

Kazumine Moriyasu, Kazuhiro Sakai, Kenichiro Yamamoto. Regular maps with the specification property. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 2991-3009. doi: 10.3934/dcds.2013.33.2991

2018 Impact Factor: 1.008

Tools

Metrics

  • PDF downloads (17)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences