An online optimization algorithm for tracking a linearly varying optimal point with zero steady-state error
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915039929171968 |
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| author | Wu, Alex Xinting Petersen, Ian R. Ugrinovskii, Valery Shames, Iman |
| author_facet | Wu, Alex Xinting Petersen, Ian R. Ugrinovskii, Valery Shames, Iman |
| contents | In this paper, we develop an online optimization algorithm for solving a class of nonconvex optimization problems with a linearly varying optimal point. The global convergence of the algorithm is guaranteed using the circle criterion for the class of functions whose gradient is bounded within a sector. Also, we show that the corresponding Luré-type nonlinear system involves a double integrator, which demonstrates its ability to track a linearly varying optimal point with zero steady-state error. The algorithm is applied to solving a time-of-arrival based localization problem with constant velocity and the results show that the algorithm is able to estimate the source location with zero steady-state error. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_01826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An online optimization algorithm for tracking a linearly varying optimal point with zero steady-state error Wu, Alex Xinting Petersen, Ian R. Ugrinovskii, Valery Shames, Iman Optimization and Control Systems and Control 93D09 In this paper, we develop an online optimization algorithm for solving a class of nonconvex optimization problems with a linearly varying optimal point. The global convergence of the algorithm is guaranteed using the circle criterion for the class of functions whose gradient is bounded within a sector. Also, we show that the corresponding Luré-type nonlinear system involves a double integrator, which demonstrates its ability to track a linearly varying optimal point with zero steady-state error. The algorithm is applied to solving a time-of-arrival based localization problem with constant velocity and the results show that the algorithm is able to estimate the source location with zero steady-state error. |
| title | An online optimization algorithm for tracking a linearly varying optimal point with zero steady-state error |
| topic | Optimization and Control Systems and Control 93D09 |
| url | https://arxiv.org/abs/2411.01826 |