Retraction maps in optimal control of nonholonomic systems
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910900921827328 |
|---|---|
| author | Simoes, Alexandre Anahory Liñán, María Barbero Bloch, Anthony Colombo, Leonardo de Diego, David Martín |
| author_facet | Simoes, Alexandre Anahory Liñán, María Barbero Bloch, Anthony Colombo, Leonardo de Diego, David Martín |
| contents | In this paper, we compare the performance of different numerical schemes in approximating Pontryagin's Maximum Principle's necessary conditions for the optimal control of nonholonomic systems. Retraction maps are used as a seed to construct geometric integrators for the corresponding Hamilton equations. First, we obtain an intrinsic formulation of a discretization map on a distribution $\mathcal{D}$. Then, we illustrate this construction on a particular example for which the performance of different symplectic integrators is examined and compared with that of non-symplectic integrators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00808 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Retraction maps in optimal control of nonholonomic systems Simoes, Alexandre Anahory Liñán, María Barbero Bloch, Anthony Colombo, Leonardo de Diego, David Martín Numerical Analysis Differential Geometry Optimization and Control In this paper, we compare the performance of different numerical schemes in approximating Pontryagin's Maximum Principle's necessary conditions for the optimal control of nonholonomic systems. Retraction maps are used as a seed to construct geometric integrators for the corresponding Hamilton equations. First, we obtain an intrinsic formulation of a discretization map on a distribution $\mathcal{D}$. Then, we illustrate this construction on a particular example for which the performance of different symplectic integrators is examined and compared with that of non-symplectic integrators. |
| title | Retraction maps in optimal control of nonholonomic systems |
| topic | Numerical Analysis Differential Geometry Optimization and Control |
| url | https://arxiv.org/abs/2504.00808 |