| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 63 | |
| Number of page(s) | 36 | |
| DOI | https://doi.org/10.1051/cocv/2024053 | |
| Published online | 10 September 2024 | |
Symmetry reduction and recovery of trajectories of optimal control problems via measure relaxations
1
Mac Team, LAAS-CNRS, Toulouse, France
2
Pop Team, LAAS-CNRS, Toulouse, France
3
Faculty of Electrical Engineering, Czech Technical University in Prague, Czechia
* Corresponding author: nicolas.augier@laas.fr
Received:
11
July
2023
Accepted:
16
July
2024
We address the problem of symmetry reduction of optimal control problems under the action of a finite group from a measure relaxation viewpoint. We propose a method based on the moment-Sum of Squares (SOS) aka Lasserre hierarchy which allows one to significantly reduce the computation time and memory requirements compared to the case without symmetry reduction. We show that the recovery of optimal trajectories boils down to solving a symmetric parametric polynomial system. Then we illustrate our method on the symmetric integrator and the time-optimal inversion of qubits.
Mathematics Subject Classification: 49M20 / 93-08 / 49M37
Key words: Optimal control / measure relaxation / semi-definite programming / symmetry reduction / invariant polynomials
© The authors. Published by EDP Sciences, SMAI 2024
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