Polynomial Turnpike Property for a Class of Infinite-Dimensional Oscillating Systems
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910038086385664 |
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| author | Zuyev, Alexander Trélat, Emmanuel |
| author_facet | Zuyev, Alexander Trélat, Emmanuel |
| contents | We establish a polynomial turnpike estimate for an optimal control problem consisting of a system of infinitely many controlled oscillators, considered as an abstract differential equation in a Hilbert space, with a quadratic cost. Our proof relies on spectral considerations and on the construction of a Riesz basis. A concrete example is given, which involves a rotating bodybeam system. To our knowledge, this is the first example of a pointwise turnpike estimate around a steady-state that is polynomial but not exponential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02067 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Polynomial Turnpike Property for a Class of Infinite-Dimensional Oscillating Systems Zuyev, Alexander Trélat, Emmanuel Optimization and Control We establish a polynomial turnpike estimate for an optimal control problem consisting of a system of infinitely many controlled oscillators, considered as an abstract differential equation in a Hilbert space, with a quadratic cost. Our proof relies on spectral considerations and on the construction of a Riesz basis. A concrete example is given, which involves a rotating bodybeam system. To our knowledge, this is the first example of a pointwise turnpike estimate around a steady-state that is polynomial but not exponential. |
| title | Polynomial Turnpike Property for a Class of Infinite-Dimensional Oscillating Systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.02067 |