Certified Learning of Incremental ISS Controllers for Unknown Nonlinear Polynomial Dynamics

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Veröffentlicht in:	arXiv.org (Dec 5, 2024), p. n/a
1. Verfasser:	Zaker, Mahdieh
Weitere Verfasser:	Angeli, David, Lavaei, Abolfazl
Veröffentlicht:	Cornell University Library, arXiv.org
Schlagworte:	System dynamics Nonlinear systems Dynamical systems Nonlinear control Liapunov functions Design optimization Controllers Nonlinear dynamics Polynomials
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Beschreibung
Abstract:	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
Quelle:	Engineering Database