Optimal control of infinite-dimensional dissipative systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918408523612160 |
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| author | Hastir, Anthony Reis, Timo |
| author_facet | Hastir, Anthony Reis, Timo |
| contents | We study the linear-quadratic optimal control problem for infinite-dimensional dissipative systems with possibly indefinite cost functional. Under the assumption that a storage function exists, we show that this indefinite optimal control problem is equivalent to a linear-quadratic optimal control problem with a nonnegative cost functional. We establish the relationship between the corresponding value functions and present the associated operator Lur'e equation. Finally, we illustrate our results with several examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_24507 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal control of infinite-dimensional dissipative systems Hastir, Anthony Reis, Timo Optimization and Control Functional Analysis 49N05, 93B28, 37L05, 93B52 We study the linear-quadratic optimal control problem for infinite-dimensional dissipative systems with possibly indefinite cost functional. Under the assumption that a storage function exists, we show that this indefinite optimal control problem is equivalent to a linear-quadratic optimal control problem with a nonnegative cost functional. We establish the relationship between the corresponding value functions and present the associated operator Lur'e equation. Finally, we illustrate our results with several examples. |
| title | Optimal control of infinite-dimensional dissipative systems |
| topic | Optimization and Control Functional Analysis 49N05, 93B28, 37L05, 93B52 |
| url | https://arxiv.org/abs/2603.24507 |