Symplectic Geometry in Hybrid and Impulsive Optimal Control
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911191021912064 |
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| author | Clark, William Oprea, Maria |
| author_facet | Clark, William Oprea, Maria |
| contents | Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory was applied to these systems and a hybrid version of Pontryagin's maximum principle was presented. This hybrid maximum principle was presented to emphasize its geometric nature which made its study amenable to the tools of geometric mechanics and symplectic geometry. One explicit benefit of this geometric approach was that the symplectic structure (and hence the induced volume) was preserved. This allowed for a hybrid analog of caustics and conjugate points. Additionally, an introductory analysis of singular solutions (beating and Zeno) was discussed geometrically. This work concluded on a biological example where beating can occur. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_15117 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symplectic Geometry in Hybrid and Impulsive Optimal Control Clark, William Oprea, Maria Optimization and Control 49N25, 34A38, 37J39 Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory was applied to these systems and a hybrid version of Pontryagin's maximum principle was presented. This hybrid maximum principle was presented to emphasize its geometric nature which made its study amenable to the tools of geometric mechanics and symplectic geometry. One explicit benefit of this geometric approach was that the symplectic structure (and hence the induced volume) was preserved. This allowed for a hybrid analog of caustics and conjugate points. Additionally, an introductory analysis of singular solutions (beating and Zeno) was discussed geometrically. This work concluded on a biological example where beating can occur. |
| title | Symplectic Geometry in Hybrid and Impulsive Optimal Control |
| topic | Optimization and Control 49N25, 34A38, 37J39 |
| url | https://arxiv.org/abs/2504.15117 |