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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.02823 |
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| _version_ | 1866915831044112384 |
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| author | Suttner, Raik Ebenbauer, Christian Dashkovskiy, Sergey |
| author_facet | Suttner, Raik Ebenbauer, Christian Dashkovskiy, Sergey |
| contents | We study the problem of global extremum seeking in the presence of local extrema. We investigate two different perturbation-based methods: 1) a well-known classical extremum seeking scheme for steady-state output optimization, and 2) a source seeking scheme for a two-dimensional point mass. In each of these two scenarios, the closed-loop system involves a damped double integrator subject to an oscillatory force. An averaging analysis reveals that the respective averaged system is again a damped double integrator, but now subject to a potential force. The potential force is given by the gradient of a locally averaged objective function. Such a function is less prone to have undesired local extrema and is therefore better suited for global optimization. We provide sufficient conditions for semi-global practical uniform asymptotic stability of the closed-loop systems. The sufficient conditions only involve assumptions on the averaged objective function but not the original one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02823 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Extremum Seeking With Double Integrators in the Presence of Local Extrema Suttner, Raik Ebenbauer, Christian Dashkovskiy, Sergey Optimization and Control We study the problem of global extremum seeking in the presence of local extrema. We investigate two different perturbation-based methods: 1) a well-known classical extremum seeking scheme for steady-state output optimization, and 2) a source seeking scheme for a two-dimensional point mass. In each of these two scenarios, the closed-loop system involves a damped double integrator subject to an oscillatory force. An averaging analysis reveals that the respective averaged system is again a damped double integrator, but now subject to a potential force. The potential force is given by the gradient of a locally averaged objective function. Such a function is less prone to have undesired local extrema and is therefore better suited for global optimization. We provide sufficient conditions for semi-global practical uniform asymptotic stability of the closed-loop systems. The sufficient conditions only involve assumptions on the averaged objective function but not the original one. |
| title | Global Extremum Seeking With Double Integrators in the Presence of Local Extrema |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.02823 |