Abstract
In this chapter we establish sufficient and necessary conditions for the turnpike phenomenon for discrete-time nonautonomous problems on subintervals of axis in metric spaces, which are not necessarily compact. For these optimal control problems the turnpike is not a singleton. We also study the existence of solutions of the corresponding infinite horizon optimal control problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aubry, S., Le Daeron, P.Y.: The discrete Frenkel-Kontorova model and its extensions I. Physica D 8, 381–422 (1983)
Carlson, D.A., Haurie, A., Leizarowitz, A.: Infinite Horizon Optimal Control. Springer, Berlin (1991)
Cesari, L.: Optimization - Theory and Applications. Springer, Berlin (1983)
Zaslavski, A.J.: Ground states in Frenkel-Kontorova model. Math. USSR Izvestiya 29, 323–354 (1987)
Zaslavski, A.J.: Turnpike Properties in the Calculus of Variations and Optimal Control. Springer, New York (2006)
Zaslavski, A.J.: Turnpike results for a discrete-time optimal control systems arising in economic dynamics. Nonlinear Anal. 67, 2024–2049 (2007)
Zaslavski, A.J.: Stability of a turnpike phenomenon for a discrete-time optimal control systems. J. Optim. Theory Appl. 145, 597–612 (2010)
Zaslavski, A.J.: Nonconvex Optimal Control and Variational Problems. Springer Optimization and Its Applications. Springer, New York (2013)
Zaslavski, A.J.: Necessary and sufficient conditions for turnpike properties of solutions of optimal control systems arising in economic dynamics. Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 20, 391–420 (2013)
Zaslavski, A.J.: Turnpike Phenomenon and Infinite Horizon Optimal Control. Springer Optimization and Its Applications. Springer, New York (2014)
Zaslavski, A.J.: Turnpike properties of approximate solutions of dynamic discrete time zero-sum games. J. Dyn. Games 2014, 299–330 (2014)
Zaslavski, A.J.: Stability of the Turnpike Phenomenon in Discrete-Time Optimal Control Problems. Springer Briefs in Optimization. Springer, New York (2014)
Zaslavski, A.J.: Turnpike Theory of Continuous-Time Linear Optimal Control Problems. Springer Optimization and Its Applications. Springer, Cham (2015)
Zaslavski, A.J.: Discrete-Time Optimal Control and Games on Large Intervals. Springer Optimization and Its Applications. Springer, Berlin (2017)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Zaslavski, A.J. (2019). Discrete-Time Nonautonomous Problems on Axis. In: Turnpike Conditions in Infinite Dimensional Optimal Control . Springer Optimization and Its Applications, vol 148. Springer, Cham. https://doi.org/10.1007/978-3-030-20178-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-20178-4_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-20177-7
Online ISBN: 978-3-030-20178-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)