article published Kathrin Flaßkamp author Sofya Maslovskaya author 87909 Sina Ober-Blöbaum author 16494 Boris Edgar Wembe Moafo author 95394 636 department <jats:title>Abstract</jats:title> <jats:p>Motivated by mechanical systems with symmetries, we focus on optimal control problems possessing certain symmetries. Following recent works (Faulwasser in Math Control Signals Syst 34:759–788 2022; Trélat in Math Control Signals Syst 35:685–739 2023), which generalized the classical concept of <jats:italic>static turnpike to manifold turnpike</jats:italic> we extend the <jats:italic>exponential turnpike property</jats:italic> to the <jats:italic>exponential trim turnpike</jats:italic> for control systems with symmetries induced by abelian or non-abelian groups. Our analysis is mainly based on the geometric reduction of control systems with symmetries. More concretely, we first reduce the control system on the quotient space and state the turnpike theorem for the reduced problem. Then we use the group properties to obtain the <jats:italic>trim turnpike theorem</jats:italic> for the full problem. Finally, we illustrate our results on the Kepler problem and the rigid body problem. </jats:p> Springer Science and Business Media LLC2025 eng 0932-4194 1435-568X10.1007/s00498-025-00408-w Flaßkamp K, Maslovskaya S, Ober-Blöbaum S, Wembe Moafo BE. Trim turnpikes for optimal control problems with symmetries. <i>Mathematics of Control, Signals, and Systems</i>. Published online 2025. doi:<a href="https://doi.org/10.1007/s00498-025-00408-w">10.1007/s00498-025-00408-w</a> K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, B.E. Wembe Moafo, Mathematics of Control, Signals, and Systems (2025). Flaßkamp, Kathrin, Sofya Maslovskaya, Sina Ober-Blöbaum, and Boris Edgar Wembe Moafo. “Trim Turnpikes for Optimal Control Problems with Symmetries.” <i>Mathematics of Control, Signals, and Systems</i>, 2025. <a href="https://doi.org/10.1007/s00498-025-00408-w">https://doi.org/10.1007/s00498-025-00408-w</a>. @article{Flaßkamp_Maslovskaya_Ober-Blöbaum_Wembe Moafo_2025, title={Trim turnpikes for optimal control problems with symmetries}, DOI={<a href="https://doi.org/10.1007/s00498-025-00408-w">10.1007/s00498-025-00408-w</a>}, journal={Mathematics of Control, Signals, and Systems}, publisher={Springer Science and Business Media LLC}, author={Flaßkamp, Kathrin and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar}, year={2025} } Flaßkamp, Kathrin, et al. “Trim Turnpikes for Optimal Control Problems with Symmetries.” <i>Mathematics of Control, Signals, and Systems</i>, Springer Science and Business Media LLC, 2025, doi:<a href="https://doi.org/10.1007/s00498-025-00408-w">10.1007/s00498-025-00408-w</a>. Flaßkamp, K., Maslovskaya, S., Ober-Blöbaum, S., &#38; Wembe Moafo, B. E. (2025). Trim turnpikes for optimal control problems with symmetries. <i>Mathematics of Control, Signals, and Systems</i>. <a href="https://doi.org/10.1007/s00498-025-00408-w">https://doi.org/10.1007/s00498-025-00408-w</a> K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, and B. E. Wembe Moafo, “Trim turnpikes for optimal control problems with symmetries,” <i>Mathematics of Control, Signals, and Systems</i>, 2025, doi: <a href="https://doi.org/10.1007/s00498-025-00408-w">10.1007/s00498-025-00408-w</a>. 597922025-05-05T09:23:38Z2025-05-05T09:24:09Z