Certified Learning of Incremental ISS Controllers for Unknown Nonlinear Polynomial Dynamics
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| Vydáno v: | arXiv.org (Dec 5, 2024), p. n/a |
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| Hlavní autor: | |
| Další autoři: | , |
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Cornell University Library, arXiv.org
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| On-line přístup: | Citation/Abstract Full text outside of ProQuest |
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| Abstrakt: | 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. |
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| ISSN: | 2331-8422 |
| Zdroj: | Engineering Database |