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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.13402 |
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| _version_ | 1866915137340833792 |
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| author | Leyendecker, Sigrid Maslovskaya, Sofya Ober-Blobaum, Sina de Almagro, Rodrigo T. Sato Martin Szemenyei, Flora Orsolya |
| author_facet | Leyendecker, Sigrid Maslovskaya, Sofya Ober-Blobaum, Sina de Almagro, Rodrigo T. Sato Martin Szemenyei, Flora Orsolya |
| contents | In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an affine control term and we allow linear coordinate changes in the configuration space. Classically, Pontryagin's maximum principle gives necessary optimality conditions for the optimal control problem. For smooth problems, alternatively, a variational approach based on an augmented objective can be followed. Here, we propose a new Lagrangian approach leading to equivalent necessary optimality conditions in the form of Euler-Lagrange equations. Thus, the differential geometric structure (similar to classical Lagrangian dynamics) can be exploited in the framework of optimal control problems. In particular, the formulation enables the symplectic discretisation of the optimal control problem via variational integrators in a straightforward way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13402 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A new Lagrangian approach to control affine systems with a quadratic Lagrange term Leyendecker, Sigrid Maslovskaya, Sofya Ober-Blobaum, Sina de Almagro, Rodrigo T. Sato Martin Szemenyei, Flora Orsolya Optimization and Control 65K10, 49M25, 65K15 In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an affine control term and we allow linear coordinate changes in the configuration space. Classically, Pontryagin's maximum principle gives necessary optimality conditions for the optimal control problem. For smooth problems, alternatively, a variational approach based on an augmented objective can be followed. Here, we propose a new Lagrangian approach leading to equivalent necessary optimality conditions in the form of Euler-Lagrange equations. Thus, the differential geometric structure (similar to classical Lagrangian dynamics) can be exploited in the framework of optimal control problems. In particular, the formulation enables the symplectic discretisation of the optimal control problem via variational integrators in a straightforward way. |
| title | A new Lagrangian approach to control affine systems with a quadratic Lagrange term |
| topic | Optimization and Control 65K10, 49M25, 65K15 |
| url | https://arxiv.org/abs/2307.13402 |