Certified Learning of Incremental ISS Controllers for Unknown Nonlinear Polynomial Dynamics
I tiakina i:
| I whakaputaina i: | arXiv.org (Dec 5, 2024), p. n/a |
|---|---|
| Kaituhi matua: | |
| Ētahi atu kaituhi: | , |
| I whakaputaina: |
Cornell University Library, arXiv.org
|
| Ngā marau: | |
| Urunga tuihono: | Citation/Abstract Full text outside of ProQuest |
| Ngā Tūtohu: |
Kāore He Tūtohu, Me noho koe te mea tuatahi ki te tūtohu i tēnei pūkete!
|
| Whakarāpopotonga: | Incremental input-to-state stability (delta-ISS) offers a robust framework to ensure that small input variations result in proportionally minor deviations in the state of a nonlinear system. This property is essential in practical applications where input precision cannot be guaranteed. However, analyzing delta-ISS demands detailed knowledge of system dynamics to assess the state's incremental response to input changes, posing a challenge in real-world scenarios where mathematical models are unknown. In this work, we develop a data-driven approach to design delta-ISS Lyapunov functions together with their corresponding delta-ISS controllers for continuous-time input-affine nonlinear systems with polynomial dynamics, ensuring the delta-ISS property is achieved without requiring knowledge of the system dynamics. In our data-driven scheme, we collect only two sets of input-state trajectories from sufficiently excited dynamics, as introduced by Willems et al.'s fundamental lemma. By fulfilling a specific rank condition, we design delta-ISS controllers using the collected samples through formulating a sum-of-squares optimization program. The effectiveness of our data-driven approach is evidenced by its application on a physical case study. |
|---|---|
| ISSN: | 2331-8422 |
| Puna: | Engineering Database |