تقرير
Minimum energy density steering of linear systems with Gromov-Wasserstein terminal cost
| العنوان: | Minimum energy density steering of linear systems with Gromov-Wasserstein terminal cost |
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| المؤلفون: | Morimoto, Kohei, Kashima, Kenji |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Electrical Engineering and Systems Science - Systems and Control |
| الوصف: | In this paper, we newly formulate and solve the optimal density control problem with Gromov-Wasserstein (GW) terminal cost in discrete-time linear Gaussian systems. Differently from the Wasserstein or Kullback-Leibler distances employed in the existing works, the GW distance quantifies the difference in shapes of the distribution, which is invariant under translation and rotation. Consequently, our formulation allows us to find small energy inputs that achieve the desired shape of the terminal distribution, which has practical applications, e.g., robotic swarms. We demonstrate that the problem can be reduced to a Difference of Convex (DC) programming, which is efficiently solvable through the DC algorithm. Through numerical experiments, we confirm that the state distribution reaches the terminal distribution that can be realized with the minimum control energy among those having the specified shape. Comment: 7 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1109/LCSYS.2024.3397228 |
| URL الوصول: | http://arxiv.org/abs/2402.15942 |
| رقم الأكسشن: | edsarx.2402.15942 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1109/LCSYS.2024.3397228 |
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