Theoretical analysis of a derivative free control based continuation algorithm with path following capability for autonomous systems
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909601181466624 |
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| author | Gourc, Etienne Caron, Romain Silva, Fabrice Vergez, Christophe Cochelin, Bruno |
| author_facet | Gourc, Etienne Caron, Romain Silva, Fabrice Vergez, Christophe Cochelin, Bruno |
| contents | We present a minimal control-based continuation algorithm designed to track branches of limit cycles in autonomous systems. The controller can be viewed as three sub-controllers: (i) a derivative feedback controller that is used to stabilize the limit cycle, (ii) an integral phase controller, used to synthesize the unknown phase of the limit cycle and (iii) an integral arclength controller, used to track branches of limit cycles. The controlled system is analyzed theoretically, using the averaging method, allowing us to express tuning rules for the different parameters of the controller. Remarkably, theses tuning rules are independent of the studied system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02262 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Theoretical analysis of a derivative free control based continuation algorithm with path following capability for autonomous systems Gourc, Etienne Caron, Romain Silva, Fabrice Vergez, Christophe Cochelin, Bruno Optimization and Control We present a minimal control-based continuation algorithm designed to track branches of limit cycles in autonomous systems. The controller can be viewed as three sub-controllers: (i) a derivative feedback controller that is used to stabilize the limit cycle, (ii) an integral phase controller, used to synthesize the unknown phase of the limit cycle and (iii) an integral arclength controller, used to track branches of limit cycles. The controlled system is analyzed theoretically, using the averaging method, allowing us to express tuning rules for the different parameters of the controller. Remarkably, theses tuning rules are independent of the studied system. |
| title | Theoretical analysis of a derivative free control based continuation algorithm with path following capability for autonomous systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2505.02262 |