Optimal control problems on the co-adjoint Lie groupoids

• Autorzy: Haghighatdoost Ghorbanali

Identyfikatory

DOI

10.24425/acs.2024.153099

• Języki publikacji: EN

Abstrakty

EN

In this work we study the invariant optimal control problem on Lie groupoids. We show that any invariant optimal control problem on a Lie groupoid reduces to its co-adjoint Lie algebroid. In the final section of the paper, we present an illustrative example.

Słowa kluczowe

EN

optimal control problem; invariant control system; Hamiltonian system; co-adjoint Lie groupoid

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2024
• Tom: Vol. 34, No. 4
• Strony: 715--742
• Opis fizyczny: Bibliogr. 14 poz., wzory

Twórcy

autor

Haghighatdoost Ghorbanali

• Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

• https://orcid.org/0000-0002-7979-6122

Bibliografia

• [1] Gh. Haghighatdoost and R. Ayoubi: Hamiltonian systems on co-adjoint Lie groupoids. Journal of Lie Theory, 31(2), (2021), 493-516.
• [2] Gh. Haghighatdoost and R. Ayoubi: Euler integrable Hamiltonian system on co-adjoint Lie groupoids. ResearchGate publications, (2021).
• [3] Gh. Haghighatdoost and R. Ayoubi: Generalized geometric Hamilton-Jacobi theorem on Lie algebroids. arXiv: 1902.06969v1, (2019). DOI: 10.48550/arXiv.1902.06969
• [4] sc M. Jozwikowski: Optimal control theory on almost Lie algebroids. PhD dissertation, Institute of Mathematics, Polish Academy of Sciences, arXiv:1111.1549v1, 2011. DOI: 10.48550/arXiv.1111.1549
• [5] J. Grabowski and M. Jozwikowski: Pontryagin maximum principle on almost Lie algebroids. SIAM Journal on Control and Optimization, 49(3), (2011), 1306-1357. DOI: 10.1137/090760246
• [6] K.C.H. Mackenzie: General theory of Lie groupoids and Lie algebroids. London Mathematical Society, Lecture notes series 213, Cambridge University Press, Cambridge, 2005.
• [7] E. Martinez: Reduction in optimal control theory. Reports on Mathematical Physics, 53(1), (2004), 79-90. DOI: 10.1016/S0034-4877(04)90005-5
• [8] J. Baillieul and J.C. Willems: (Eds.) Mathematical Control Theory. Springer-Verlag New York, Inc. 1999.
• [9] H.J. Sussmann: Geometry and Optimal Control, Mathematical Control Theory. Book of essays a in honor of Roger W. Brockett on the o ccasion of his 60th birthday. J. Baillieul and J.C. Willems (Eds.), Springer-Verlag, 1998.
• [10] V. Jurdjevic: Geometric Control Theory. Cambridge University Press, 1997.
• [11] V. Jurdjevic: Optimal control problems on Lie groups: Crossroads between geometry and mechanics. In B. Jakubczyk and W. Respondek (Eds.), Geometry of Feedback and Optimal Control, Marcel-Dekker, 1993.
• [12] M. de Leon, J. C. Marrero and E. Martinez: Lagrangian submanifolds and dynamics on Lie algebroids. Journal of Physics A: Mathematical and General, 38(24), (2005), 241-308. DOI: 10.1088/0305-4470/38/24/R01
• [13] J.C. Marrero: Hamiltonian dynamics on Lie algebroids, unimodularity and preservation of volumes. arXiv preprint arXiv:0905.0123v1, (2009). DOI: 10.48550/arXiv.0905.0123
• [14] R. Bos: Geometric quantization of Hamiltonian actions of Lie algebroids and Lie groupoids. International Journal of Geometric Methods in Modern Physics, 4(3), (2007), 389-436. DOI: 10.1142/S0219887807002077

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025)