Guaranteed Time Control using Linear Matrix Inequalities
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910141171892224 |
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| author | Campos, Víctor Costa da Silva Quadros, Mariella Maia Frezzato, Luciano Mozelli, Leonardo Nguyen, Anh-Tu |
| author_facet | Campos, Víctor Costa da Silva Quadros, Mariella Maia Frezzato, Luciano Mozelli, Leonardo Nguyen, Anh-Tu |
| contents | This paper presents a synthesis approach aiming to guarantee a minimum upper-bound for the time taken to reach a target set of non-zero measure that encompasses the origin, while taking into account uncertainties and input and state constraints. This approach is based on a harmonic transformation of the Lyapunov function and a novel piecewise quadratic representation of this transformed Lyapunov function over a simplicial partition of the state space. The problem is solved in a policy iteration fashion, whereas the evaluation and improvement steps are formulated as linear matrix inequalities employing the structural relaxation approach. Though initially formulated for uncertain polytopic systems, extensions to piecewise and nonlinear systems are discussed. Three examples illustrate the effectiveness of the proposed approach in different scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02636 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Guaranteed Time Control using Linear Matrix Inequalities Campos, Víctor Costa da Silva Quadros, Mariella Maia Frezzato, Luciano Mozelli, Leonardo Nguyen, Anh-Tu Systems and Control This paper presents a synthesis approach aiming to guarantee a minimum upper-bound for the time taken to reach a target set of non-zero measure that encompasses the origin, while taking into account uncertainties and input and state constraints. This approach is based on a harmonic transformation of the Lyapunov function and a novel piecewise quadratic representation of this transformed Lyapunov function over a simplicial partition of the state space. The problem is solved in a policy iteration fashion, whereas the evaluation and improvement steps are formulated as linear matrix inequalities employing the structural relaxation approach. Though initially formulated for uncertain polytopic systems, extensions to piecewise and nonlinear systems are discussed. Three examples illustrate the effectiveness of the proposed approach in different scenarios. |
| title | Guaranteed Time Control using Linear Matrix Inequalities |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2510.02636 |