A Complete Inverse Optimality Study for a Tank-Liquid System
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910460118302720 |
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| author | Karafyllis, Iasson Vokos, Filippos Krstic, Miroslav |
| author_facet | Karafyllis, Iasson Vokos, Filippos Krstic, Miroslav |
| contents | This paper presents a complete inverse optimality study for a linearized tank-liquid system where the liquid is described by the viscous Saint-Venant model with surface tension and possible wall friction. We define an appropriate weak solution notion for which we establish existence/uniqueness results with inputs that do not necessarily satisfy any compatibility condition as well as stabilization results with feedback laws that are constructed with the help of a Control Lyapunov Functional. We show that the proposed family of stabilizing feedback laws is optimal for a certain meaningful quadratic cost functional. Finally, we show that the optimal feedback law guarantees additional stronger stability estimates which are similar to those obtained in the case of classical solutions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_16535 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Complete Inverse Optimality Study for a Tank-Liquid System Karafyllis, Iasson Vokos, Filippos Krstic, Miroslav Optimization and Control Systems and Control Analysis of PDEs 93C20, 93B52, 49N45, 35G16 This paper presents a complete inverse optimality study for a linearized tank-liquid system where the liquid is described by the viscous Saint-Venant model with surface tension and possible wall friction. We define an appropriate weak solution notion for which we establish existence/uniqueness results with inputs that do not necessarily satisfy any compatibility condition as well as stabilization results with feedback laws that are constructed with the help of a Control Lyapunov Functional. We show that the proposed family of stabilizing feedback laws is optimal for a certain meaningful quadratic cost functional. Finally, we show that the optimal feedback law guarantees additional stronger stability estimates which are similar to those obtained in the case of classical solutions. |
| title | A Complete Inverse Optimality Study for a Tank-Liquid System |
| topic | Optimization and Control Systems and Control Analysis of PDEs 93C20, 93B52, 49N45, 35G16 |
| url | https://arxiv.org/abs/2405.16535 |