Abstract
We consider the turnpike property for infinite horizon undiscounted optimal control problems in discrete time and with time-varying data. We show that, under suitable conditions, a time-varying strict dissipativity notion implies the turnpike property and a continuity property of the optimal value function. We also discuss the relation of strict dissipativity to necessary optimality conditions and illustrate our results by an example.
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Notes
- 1.
In particular in the economic literature, this property is also referred to as catching up optimality, see e.g. Bewley (2009).
- 2.
Introduced in the context of control systems by Jan Willems in 1972, see Willems (1972).
- 3.
The proof uses a construction similar to the one of Lemma 6.3 in Grüne (2013).
- 4.
The idea is similar to the proof of Theorem 16 in Müller and Grüne (2016).
- 5.
This means that dissipativity holds for all \(x\in \mathbb {X}_0\).
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Acknowledgements
The research was supported by the DFG Grants GR1569/13-1 and 16-1.
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Grüne, L., Pirkelmann, S., Stieler, M. (2018). Strict Dissipativity Implies Turnpike Behavior for Time-Varying Discrete Time Optimal Control Problems. In: Feichtinger, G., Kovacevic, R., Tragler, G. (eds) Control Systems and Mathematical Methods in Economics. Lecture Notes in Economics and Mathematical Systems, vol 687. Springer, Cham. https://doi.org/10.1007/978-3-319-75169-6_10
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