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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2412.20362 |
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| _version_ | 1866915084109873152 |
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| author | Mesquita, Jaqueline G. Oliveira, Tiago Roux Reis, Henrique C. dos |
| author_facet | Mesquita, Jaqueline G. Oliveira, Tiago Roux Reis, Henrique C. dos |
| contents | This paper investigates a new class of equations called measure functional differential equations with state-dependent delays. We establish the existence and uniqueness of solutions and present a discussion concerning the appropriate phase space to define these equations. Also, we prove a version of periodic averaging principle to these equations. This type of result was completely open in the literature. These equations involving measure bring the advantage to encompass others such as impulsive, dynamic equations on time scales and difference equations, expanding their application potential. Additionally, we apply our theoretical insights to a real-time optimization strategy, using extremum seeking to validate the stability of an innovative algorithm under state-dependent delays. This application confirm the relevance of our findings in practical scenarios, offering valuable tools for advanced control system design. Our research provides significant contributions to the mathematical field and suggests new directions for future technological developments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20362 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Slow and fast dynamics in measure functional differential equations with state-dependent delays through averaging principles and applications to extremum seeking Mesquita, Jaqueline G. Oliveira, Tiago Roux Reis, Henrique C. dos Optimization and Control Systems and Control 34K33, 34C25, 26E70 This paper investigates a new class of equations called measure functional differential equations with state-dependent delays. We establish the existence and uniqueness of solutions and present a discussion concerning the appropriate phase space to define these equations. Also, we prove a version of periodic averaging principle to these equations. This type of result was completely open in the literature. These equations involving measure bring the advantage to encompass others such as impulsive, dynamic equations on time scales and difference equations, expanding their application potential. Additionally, we apply our theoretical insights to a real-time optimization strategy, using extremum seeking to validate the stability of an innovative algorithm under state-dependent delays. This application confirm the relevance of our findings in practical scenarios, offering valuable tools for advanced control system design. Our research provides significant contributions to the mathematical field and suggests new directions for future technological developments. |
| title | Slow and fast dynamics in measure functional differential equations with state-dependent delays through averaging principles and applications to extremum seeking |
| topic | Optimization and Control Systems and Control 34K33, 34C25, 26E70 |
| url | https://arxiv.org/abs/2412.20362 |