A tutorial on Pontryagin-Koopman operators for infinite horizon optimal control

Authors

Y. Guo, B. Houska, M.E. Villanueva

Reference

In Proceedings of the 61st IEEE Conference on Decision and Control,
Cancún, Mexico, pages 6800–6805, December, 2022.

Abstract

This paper provides a tutorial on how to use Koopman operators to lift Pontryagin's optimality condition for infinite-horizon optimal control problems into an infinite dimensional space. It is shown how to exploit the symplectic structure of the associated Pontryagin-Koopman operator in order to identify the stable manifold on which optimal trajectories evolve. Moreover, it is shown how to conduct a Koopman mode analysis in order to characterize optimal feedback control laws. Our focus is on providing a review of and gain further insight into the theory of Koopman-operator based optimal control methods. This is achieved by exploiting the structure of a particular optimal regulation problem, which is used as a tutorial example throughout the paper.

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Bibtex

@INPROCEEDINGS{Guo2022,
author = {Guo, Y. and Houska, B. and Villanueva, M.E.},
title = {A tutorial on Pontryagin-Koopman operators for infinite horizon optimal control},
booktitle = {In Proceedings of the 61st IEEE Conference on Decision and Control},
year = {2022},
pages = {6800–6805},
}