Certified Learning of Incremental ISS Controllers for Unknown Nonlinear Polynomial Dynamics
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| Pubblicato in: | arXiv.org (Dec 5, 2024), p. n/a |
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| Autore principale: | |
| Altri autori: | , |
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Cornell University Library, arXiv.org
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| Accesso online: | Citation/Abstract Full text outside of ProQuest |
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|---|---|---|---|
| 001 | 3141682444 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2331-8422 | ||
| 035 | |a 3141682444 | ||
| 045 | 0 | |b d20241205 | |
| 100 | 1 | |a Zaker, Mahdieh | |
| 245 | 1 | |a Certified Learning of Incremental ISS Controllers for Unknown Nonlinear Polynomial Dynamics | |
| 260 | |b Cornell University Library, arXiv.org |c Dec 5, 2024 | ||
| 513 | |a Working Paper | ||
| 520 | 3 | |a 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. | |
| 653 | |a System dynamics | ||
| 653 | |a Nonlinear systems | ||
| 653 | |a Dynamical systems | ||
| 653 | |a Nonlinear control | ||
| 653 | |a Liapunov functions | ||
| 653 | |a Design optimization | ||
| 653 | |a Controllers | ||
| 653 | |a Nonlinear dynamics | ||
| 653 | |a Polynomials | ||
| 700 | 1 | |a Angeli, David | |
| 700 | 1 | |a Lavaei, Abolfazl | |
| 773 | 0 | |t arXiv.org |g (Dec 5, 2024), p. n/a | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3141682444/abstract/embedded/ZKJTFFSVAI7CB62C?source=fedsrch |
| 856 | 4 | 0 | |3 Full text outside of ProQuest |u http://arxiv.org/abs/2412.03901 |