A Stability Condition for Online Feedback Optimization without Timescale Separation
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915383632461824 |
|---|---|
| author | Bianchi, Mattia Dörfler, Florian |
| author_facet | Bianchi, Mattia Dörfler, Florian |
| contents | Online Feedback Optimization (OFO) is a control approach to drive a dynamical plant to an optimal steady state. By interconnecting optimization algorithms with real-time plant measurements, OFO provides all the benefits of feedback control, yet without requiring exact knowledge of plant dynamics for computing a setpoint. On the downside, existing stability guarantees for OFO require the controller to evolve on a sufficiently slower timescale than the plant, possibly affecting transient performance and responsiveness to disturbances. In this paper, we prove that, under suitable conditions, OFO ensures stability without any timescale separation. In particular, the condition we propose is independent of the time constant of the plant, hence it is scaling-invariant. Our analysis leverages a composite Lyapunov function, which is the $\max$ of plant-related and controller-related components. We corroborate our theoretical results with numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Stability Condition for Online Feedback Optimization without Timescale Separation Bianchi, Mattia Dörfler, Florian Optimization and Control Systems and Control Dynamical Systems Online Feedback Optimization (OFO) is a control approach to drive a dynamical plant to an optimal steady state. By interconnecting optimization algorithms with real-time plant measurements, OFO provides all the benefits of feedback control, yet without requiring exact knowledge of plant dynamics for computing a setpoint. On the downside, existing stability guarantees for OFO require the controller to evolve on a sufficiently slower timescale than the plant, possibly affecting transient performance and responsiveness to disturbances. In this paper, we prove that, under suitable conditions, OFO ensures stability without any timescale separation. In particular, the condition we propose is independent of the time constant of the plant, hence it is scaling-invariant. Our analysis leverages a composite Lyapunov function, which is the $\max$ of plant-related and controller-related components. We corroborate our theoretical results with numerical examples. |
| title | A Stability Condition for Online Feedback Optimization without Timescale Separation |
| topic | Optimization and Control Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2412.10964 |