| Autor: |
Mahdi H. Azad, Nima Assadian |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
IEEE Access, Vol 12, Pp 141671-141684 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2169-3536 |
| DOI: |
10.1109/ACCESS.2024.3465220 |
| Popis: |
In this paper, we address the optimal transport problem over a linear quadratic regulator with free-final-states (the free OT-LQR problem). We prove the existence and uniqueness of the solution and discuss the regularity conditions for the optimal transport map. To provide a comparative perspective, we introduce a novel method to prove results for the solution to the optimal transport over LQR with fixed-final-states (the fixed OT-LQR problem), results that existing approaches cannot prove. We show that almost all optimal trajectories of the fixed OT-LQR problem do not intersect with any other optimal trajectories. Additionally, when the initial and final measures are absolutely continuous, the optimal induced measure remains absolutely continuous at all intermediate times. We further establish that a result analogous to Bellman’s principle of optimality holds for the fixed OT-LQR problem. Comparing the fixed and free OT-LQR problems, we find that, despite similarities in existence and uniqueness, the dependence of the Lagrangian in the free OT-LQR problem on free-final-states leads to significant differences in the properties of their solutions. This distinction indicates that both the established methods in the literature and the new methods presented for the fixed OT-LQR problem cannot be directly applied to the free OT-LQR problem. Finally, we present two numerical examples of the free OT-LQR problem. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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