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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.14046 |
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| _version_ | 1866912280520687616 |
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| author | Acquistapace, Paolo Bucci, Francesca |
| author_facet | Acquistapace, Paolo Bucci, Francesca |
| contents | A study of the linear quadratic (LQ) control problem on a finite time interval for a model equation in Hilbert spaces which comprehends the memory of the inputs was performed recently by the authors. The outcome included a closed-loop representation of the unique optimal control, along with the derivation of a related coupled system of three quadratic (operator) equations which is shown to be well-posed. Notably, in the absence of memory the above elements -- namely, formula and system -- reduce to the known feedback formula and single differential Riccati equation, respectively. In this work we take the next natural step, and prove the said results for a class of evolutions where the control operator is no longer bounded. These findings appear to be the first ones of their kind; furthermore, they extend the classical theory of the LQ problem and Riccati equations for parabolic partial differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14046 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear quadratic control of parabolic-like evolutions with memory of the inputs Acquistapace, Paolo Bucci, Francesca Optimization and Control 49N10, 35R09, 93C23, 49N35 A study of the linear quadratic (LQ) control problem on a finite time interval for a model equation in Hilbert spaces which comprehends the memory of the inputs was performed recently by the authors. The outcome included a closed-loop representation of the unique optimal control, along with the derivation of a related coupled system of three quadratic (operator) equations which is shown to be well-posed. Notably, in the absence of memory the above elements -- namely, formula and system -- reduce to the known feedback formula and single differential Riccati equation, respectively. In this work we take the next natural step, and prove the said results for a class of evolutions where the control operator is no longer bounded. These findings appear to be the first ones of their kind; furthermore, they extend the classical theory of the LQ problem and Riccati equations for parabolic partial differential equations. |
| title | Linear quadratic control of parabolic-like evolutions with memory of the inputs |
| topic | Optimization and Control 49N10, 35R09, 93C23, 49N35 |
| url | https://arxiv.org/abs/2503.14046 |