Title data
Faulwasser, Timm ; Grüne, Lars:
Turnpike Properties in Optimal Control : An Overview of DiscreteTime and ContinuousTime Results.
In: Trélat, Emmanuel ; Zuazua, Enrique
(ed.):
Handbook of Numerical Analysis : Numerical Control. Part A. 
Amsterdam
: NorthHolland
,
2022
.  pp. 367400
.  (Handbook of Numerical Analysis
; 23
)
DOI: https://doi.org/10.1016/bs.hna.2021.12.011
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The turnpike property refers to the phenomenon that in many optimal control problems, the solutions for different initial conditions and varying horizons approach a neighborhood of a specific steady state, then stay in this neighborhood for the major part of the time horizon, until they may finally depart. While early observations of the phenomenon can be traced back to works of Ramsey and von Neumann on problems in economics in 1928 and 1938, the turnpike property received continuous interest in economics since the 1960s and recent interest in systems and control. The present chapter provides an introductory overview of discretetime and continuoustime results in finite and infinitedimensions. We comment on dissipativitybased approaches and infinitehorizon results, which enable the exploitation of turnpike properties for the numerical solution of problems with long and infinite horizons. After drawing upon numerical examples, the chapter concludes with an outlook on timevarying, discounted, and open problems.
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Turnpike Properties in Optimal Control : An Overview of DiscreteTime and ContinuousTime Results. (deposited 01 Dec 2020 09:12)
 Turnpike Properties in Optimal Control : An Overview of DiscreteTime and ContinuousTime Results. (deposited 11 Feb 2022 12:58) [Currently Displayed]