Certified Learning of Incremental ISS Controllers for Unknown Nonlinear Polynomial Dynamics
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 precise 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. 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 to a physical case study.
Cite
@article{arxiv.2412.03901,
title = {Certified Learning of Incremental ISS Controllers for Unknown Nonlinear Polynomial Dynamics},
author = {Mahdieh Zaker and David Angeli and Abolfazl Lavaei},
journal= {arXiv preprint arXiv:2412.03901},
year = {2025}
}