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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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Table of 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.