Optimal Control for Minimizing Inescapable Ellipsoids in Linear Periodically Time-Varying Systems Under Bounded Disturbances
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914022228492288 |
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| author | Dogadin, Egor Peregudin, Alexey |
| author_facet | Dogadin, Egor Peregudin, Alexey |
| contents | This letter addresses optimal controller design for periodic linear time-varying systems under unknown-but-bounded disturbances. We introduce differential Lyapunov-type equations to describe time-varying inescapable ellipsoids and define an integral-based measure of their size. To minimize this measure, we develop a differential Riccati equation-based approach that provides exact solutions for state-feedback, observer synthesis, and output-feedback control. A key component is a systematic procedure for determining the optimal time-varying parameter, reducing an infinite-dimensional optimization to a simple iterative process. A numerical example validates the method's effectiveness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Control for Minimizing Inescapable Ellipsoids in Linear Periodically Time-Varying Systems Under Bounded Disturbances Dogadin, Egor Peregudin, Alexey Optimization and Control Systems and Control This letter addresses optimal controller design for periodic linear time-varying systems under unknown-but-bounded disturbances. We introduce differential Lyapunov-type equations to describe time-varying inescapable ellipsoids and define an integral-based measure of their size. To minimize this measure, we develop a differential Riccati equation-based approach that provides exact solutions for state-feedback, observer synthesis, and output-feedback control. A key component is a systematic procedure for determining the optimal time-varying parameter, reducing an infinite-dimensional optimization to a simple iterative process. A numerical example validates the method's effectiveness. |
| title | Optimal Control for Minimizing Inescapable Ellipsoids in Linear Periodically Time-Varying Systems Under Bounded Disturbances |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2509.04090 |