Multivariable Extremum Seeking Unit-Vector Control Design
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916682727948288 |
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| author | Silva, Enzo Ferreira Tomaz Coutinho, Pedro Henrique Silva Oliveira, Tiago Roux Krstić, Miroslav |
| author_facet | Silva, Enzo Ferreira Tomaz Coutinho, Pedro Henrique Silva Oliveira, Tiago Roux Krstić, Miroslav |
| contents | This paper investigates multivariable extremum seeking using unit-vector control. By employing the gradient algorithm and a polytopic embedding of the unknown Hessian matrix, we establish sufficient conditions, expressed as linear matrix inequalities, for designing the unit-vector control gain that ensures finite-time stability of the origin of the average closed-loop error system. Notably, these conditions enable the design of non-diagonal control gains, which provide extra degrees of freedom to the solution. The convergence of the actual closed-loop system to a neighborhood of the unknown extremum point is rigorously proven through averaging analysis for systems with discontinuous right-hand sides. Numerical simulations illustrate the efficacy of the proposed extremum seeking control algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07251 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multivariable Extremum Seeking Unit-Vector Control Design Silva, Enzo Ferreira Tomaz Coutinho, Pedro Henrique Silva Oliveira, Tiago Roux Krstić, Miroslav Optimization and Control Systems and Control This paper investigates multivariable extremum seeking using unit-vector control. By employing the gradient algorithm and a polytopic embedding of the unknown Hessian matrix, we establish sufficient conditions, expressed as linear matrix inequalities, for designing the unit-vector control gain that ensures finite-time stability of the origin of the average closed-loop error system. Notably, these conditions enable the design of non-diagonal control gains, which provide extra degrees of freedom to the solution. The convergence of the actual closed-loop system to a neighborhood of the unknown extremum point is rigorously proven through averaging analysis for systems with discontinuous right-hand sides. Numerical simulations illustrate the efficacy of the proposed extremum seeking control algorithm. |
| title | Multivariable Extremum Seeking Unit-Vector Control Design |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2504.07251 |