Polynomial Approximation for Data-Driven System Analysis and Control of Nonlinear Systems

By Tim Martin

This thesis presents data-driven methods for nonlinear systems, enabling the verification of system-theoretical properties and the design of state feedbacks based on measured trajectories. Despite noisy data, the developed methods provide rigorous guarantees and leverage convex optimization. Classical control techniques require a mathematical model of the system dynamics, which derivation from first principles often demands expert knowledge or is time-consuming. In contrast, data-based control methods determine system properties and controllers from system trajectories. Whereas recent developments address linear systems, dynamical systems are generally nonlinear in practice. Therefore, this thesis first introduces a data-based system representation for unknown polynomial systems to determine dissipativity and integral quadratic constraints via sum-of-squares optimization. The second part of the thesis establishes a polynomial representation of nonlinear systems based on polynomial interpolation. Due to the unknown interpolation polynomial, a set of polynomials containing the actual interpolation polynomial is deduced from noisy data. This set, along with a polynomial bound on the approximation error, forms the basis for determining dissipativity properties and designing state feedbacks with stability guarantees utilizing robust control techniques and sum-of-squares relaxation.

• Format: Paperback
• Language: English
• ISBN: 3832558861
• ISBN13: 9783832558864
• Release Date: December 2024
• Publisher: Logos Verlag Berlin
• Length: 193 Pages
• Weight: 0.88 lbs.
• Dimensions: 0.5" x 5.7" x 8.0"