The Cesàro Value Iteration

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Original languageEnglish
Pages (from-to)1934 - 1939
Number of pages6
JournalIEEE Control Systems Letters
Volume9
Early online date1 Jul 2025
Publication statusPublished - 29 Jul 2025

Abstract

In this letter, we consider undiscouted infinite-horizon optimal control for deterministic systems with an uncountable state and input space. We specifically address the case when the classic value iteration does not converge. For such systems, we use the Cesàro mean to define the infinite-horizon optimal control problem and the corresponding infinite-horizon value function. Moreover, for this value function, we introduce the Cesàro value iteration and prove its convergence for the special case of systems with periodic optimal operating behavior. For this instance, we also show that the Cesàro value function recovers the undiscounted infinite-horizon optimal cost, if the latter is well-defined.

Keywords

    average reward, Cesàro mean, Optimal control, value iteration

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The Cesàro Value Iteration. / Mair, Jonas; Schwenkel, Lukas; Müller, Matthias A. et al.
In: IEEE Control Systems Letters, Vol. 9, 29.07.2025, p. 1934 - 1939.

Research output: Contribution to journalArticleResearchpeer review

Mair, J, Schwenkel, L, Müller, MA & Allgöwer, F 2025, 'The Cesàro Value Iteration', IEEE Control Systems Letters, vol. 9, pp. 1934 - 1939. https://doi.org/10.1109/LCSYS.2025.3584792, https://doi.org/10.48550/arXiv.2504.04889
Mair, J., Schwenkel, L., Müller, M. A., & Allgöwer, F. (2025). The Cesàro Value Iteration. IEEE Control Systems Letters, 9, 1934 - 1939. https://doi.org/10.1109/LCSYS.2025.3584792, https://doi.org/10.48550/arXiv.2504.04889
Mair J, Schwenkel L, Müller MA, Allgöwer F. The Cesàro Value Iteration. IEEE Control Systems Letters. 2025 Jul 29;9:1934 - 1939. Epub 2025 Jul 1. doi: 10.1109/LCSYS.2025.3584792, 10.48550/arXiv.2504.04889
Mair, Jonas ; Schwenkel, Lukas ; Müller, Matthias A. et al. / The Cesàro Value Iteration. In: IEEE Control Systems Letters. 2025 ; Vol. 9. pp. 1934 - 1939.
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