Optimal Control of Hybrid Systems with Submersive Resets
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914719387877376 |
|---|---|
| author | Clark, William Oprea, Maria Shaw, Aden |
| author_facet | Clark, William Oprea, Maria Shaw, Aden |
| contents | Hybrid dynamical systems are systems which posses both continuous and discrete transitions. Assuming that the discrete transitions (resets) occur a finite number of times, the optimal control problem can be solved by gluing together the optimal arcs from the underlying continuous problem via the "Hamilton jump conditions." In most cases, it is assumed that the reset is a diffeomorphism (onto its image) and the corresponding Hamilton jump condition admits a unique solution. However, in many applications, the reset results in a drop in dimension and the corresponding Hamilton jump condition admits zero/infinitely many solutions. A geometric interpretation of this issue is explored in the case where the reset is a submersion (onto its image). Necessary conditions are presented for this case along with an accompanying numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Control of Hybrid Systems with Submersive Resets Clark, William Oprea, Maria Shaw, Aden Optimization and Control 93C30 (Primary) 49N25 (Secondary) Hybrid dynamical systems are systems which posses both continuous and discrete transitions. Assuming that the discrete transitions (resets) occur a finite number of times, the optimal control problem can be solved by gluing together the optimal arcs from the underlying continuous problem via the "Hamilton jump conditions." In most cases, it is assumed that the reset is a diffeomorphism (onto its image) and the corresponding Hamilton jump condition admits a unique solution. However, in many applications, the reset results in a drop in dimension and the corresponding Hamilton jump condition admits zero/infinitely many solutions. A geometric interpretation of this issue is explored in the case where the reset is a submersion (onto its image). Necessary conditions are presented for this case along with an accompanying numerical example. |
| title | Optimal Control of Hybrid Systems with Submersive Resets |
| topic | Optimization and Control 93C30 (Primary) 49N25 (Secondary) |
| url | https://arxiv.org/abs/2401.14476 |