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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/2601.02607 |
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| _version_ | 1866909982201479168 |
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| author | Muchave, Elisio Juvenal Coutinho, Pedro Henrique Silva Oliveira, Tiago Roux Krstić, Miroslav |
| author_facet | Muchave, Elisio Juvenal Coutinho, Pedro Henrique Silva Oliveira, Tiago Roux Krstić, Miroslav |
| contents | This paper deals with the gradient-based extremum seeking control (ESC) with actuation dynamics governed by distributed wave partial differential equations (PDEs). To achieve the control objective of real-time optimization for this class of infinite-dimensional systems, we first solve the trajectory generation problem to re-design the additive perturbation signal of the ESC system. Then, we develop a boundary control law through the backstepping method to compensate for the wave PDE with distributed effects, which ensures the exponential stability of the average closed-loop system by means of a Lyapunov-based analysis. At last, by employing the averaging theory for infinite-dimensional systems, we prove that the closed-loop trajectories converge to a small neighborhood surrounding the optimal point. Numerical simulations are presented to illustrate the effectiveness of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02607 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Extremum Seeking Control for Wave-PDE Actuation with Distributed Effects Muchave, Elisio Juvenal Coutinho, Pedro Henrique Silva Oliveira, Tiago Roux Krstić, Miroslav Optimization and Control Systems and Control This paper deals with the gradient-based extremum seeking control (ESC) with actuation dynamics governed by distributed wave partial differential equations (PDEs). To achieve the control objective of real-time optimization for this class of infinite-dimensional systems, we first solve the trajectory generation problem to re-design the additive perturbation signal of the ESC system. Then, we develop a boundary control law through the backstepping method to compensate for the wave PDE with distributed effects, which ensures the exponential stability of the average closed-loop system by means of a Lyapunov-based analysis. At last, by employing the averaging theory for infinite-dimensional systems, we prove that the closed-loop trajectories converge to a small neighborhood surrounding the optimal point. Numerical simulations are presented to illustrate the effectiveness of the proposed method. |
| title | Extremum Seeking Control for Wave-PDE Actuation with Distributed Effects |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2601.02607 |